d'échange dans le graphène tout en conservant sa dispersion électronique linéaire. Dans ce travail, nous nous concentrons sur l'interface entre le graphène et une monocouche de cobalt (Co) ou un alliage cobalt-iridium (CoIr). L'alliage peut être utilisé pour ajuster la force moyenne de l'interaction tout en préservant la magnétisation globale du système.

. Dans ce travail, notre stratégie consiste à augmenter l'interaction d'un matériau à fort spin-orbite avec le graphène. À cet égard, le palladium (Pd) est un bon candidat, car il possède une interaction intermédiaire avec le graphène (supérieure à l'or, inférieure au Co pour empêcher la destruction du cône de Dirac) et un couplage spin-orbite intrinsèque intermédiaire.

L'étude présentée dans cette thèse se concentre sur l'interaction du graphène avec des monocouches atomiques. De tels systèmes hybrides permettent d'accéder à un nouveau paramètre pour l'ingénierie de bande : le paramètre de maille de la monocouche.

Comme il est détaillé plus loin, le graphène est d'abord construit sur un substrat Ir(111).

.

. Ainsi, avec une telle procédure, la commensurabilité entre le graphène et son substrat peut être modifiée, devenant un nouveau paramètre pour l'ingénierie de bande. Bien évidemment, cela requiert des années d'expériences pour trouver les conditions de croissance optimales.

Pour cette raison, nous nous concentrons sur l'intercalation de monocouche atomique qui représente le point de départ d'une telle étude.

Ce manuscrit de thèse se développe selon la progression suivante.

. La commensurabilité entre le graphène et la sous-couche intercalée peut donc être ajustée, ce qui permet d'adapter le décalage du réseau à l'interface graphène/métal. Ceci représente un paramètre clé pour l'hybridation électronique, car il influence fortement le recouvrement des fonctions d'onde à l'interface.

Résumé en français

Au cours des dernières décennies, l'étude des propriétés physiques et chimiques des systèmes de faible dimensionnalité s'est accrue grâce à une avancée technologique extraordinaire et rapide. Pour la première fois, il a été possible d'étudier et de concevoir des structures jusqu'au niveau atomique où se déroulent des phénomènes fascinants. Il a été démontré que la réduction de la taille et de la dimensionnalité aboutit souvent à de toutes nouvelles propriétés mécaniques [START_REF] Tolbert | High-pressure structural transformations in semiconductor nanocrystals[END_REF][START_REF] Wong | Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes[END_REF][START_REF] Akinwande | A review on mechanics and mechanical properties of 2d materials-graphene and beyond[END_REF], optiques [START_REF] Wilcoxon | Photoluminescence from nanosize gold clusters[END_REF][START_REF] Yao | Large optical activity of gold nanocluster enantiomers induced by a pair of optically active penicillamines[END_REF], électroniques [START_REF] Shipway | Nanoparticle arrays on surfaces for electronic, optical, and sensor applications[END_REF][START_REF] Gittins | A nanometre-scale electronic switch consisting of a metal cluster and redox-addressable groups[END_REF] et magnétiques [START_REF] Leslie-Pelecky | Magnetic properties of nanostructured materials[END_REF][START_REF] Gambardella | Giant magnetic anisotropy of single cobalt atoms and nanoparticles[END_REF] des matériaux. Cela fait de la nanoscience et de la nanotechnologie l'un des domaines de recherche les plus importants, pour des perspectives à la fois fondamentales et applicatives.

Parmi les différents domaines de recherche sur les systèmes de basse dimensionnalité, la recherche scientifique sur le graphène (Gr) a été particulièrement active. L'attrait pour ce matériau provient du large éventail d'applications possibles [START_REF] Chung | Biomedical applications of graphene and graphene oxide[END_REF][START_REF] Huang | An overview of the applications of graphenebased materials in supercapacitors[END_REF][START_REF] Perreault | Environmental applications of graphene-based nanomaterials[END_REF][START_REF] Bae | Towards industrial applications of graphene electrodes[END_REF][START_REF] Palacios | Applications of graphene devices in rf communications[END_REF], tant par ses propriétés mécaniques [START_REF] Bizao | Mechanical properties of graphene nanowiggles[END_REF][START_REF] Lee | Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene[END_REF] et électroniques exceptionnelles [START_REF] Novoselov | The electronic properties of graphene[END_REF][START_REF] Geim | The rise of graphene[END_REF][START_REF] Geim | Graphene : Status and Prospects[END_REF]. Le graphène, un allotrope bidimensionnel du carbone, présente en effet une mobilité électronique exceptionnellement élevée, provenant de la dispersion linéaire de sa bande électronique issue des orbitales π, appelée cône de Dirac. La vitesse des électrons est environ 150 fois plus grande dans le graphène que dans le silicium, ce qui devrait permettre d'améliorer considérablement les performances des dispositifs électroniques de nouvelle génération. De plus, le graphène est en carbone, un matériau bon marché et abondant, offrant une alternative écologique et économique à la technologie actuelle.

Toutefois, pour pouvoir utiliser le graphène dans des dispositifs pleinement développés, il est nécessaire de modifier ses propriétés électroniques, par exemple par l'ouverture d'une bande d'énergie interdite ("gap") ou la polarisation en spin de sa structure de bande.

Cette nécessité a fait de l'ingénierie de bande du graphène un domaine de recherche très actif au cours des quinze dernières années.

vi Résumé en francais vii En ce qui concerne les applications des systèmes de basse dimensionnalité, l'une des plus intéressantes est la spintronique, qui vise à utiliser le degré de liberté de spin des électrons pour de nouvelles formes de stockage d'informations et de dispositifs logiques. L'étape fondatrice de la spintronique a été la découverte de la magnétorésistance géante dans des structures en couches minces [START_REF] Baibich | Giant magnetoresistance of (001) fe/(001) cr magnetic superlattices[END_REF][START_REF] Binasch | Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange[END_REF], qui a eu un impact technologique considérable dans les capteurs de champ magnétique, actuellement utilisés dans les disques durs, les biocapteurs, les systèmes microélectromécaniques et les mémoires magnétorésistives à accès aléatoire. Le domaine de la spintronique connaît aujourd'hui une deuxième révolution après la découverte de l'effet de couple de transfert de spin, qui permet de contrôler la magnétisation avec du courant électrique [START_REF] Myers | Currentinduced switching of domains in magnetic multilayer devices[END_REF][START_REF] Berger | Emission of spin waves by a magnetic multilayer traversed by a current[END_REF][START_REF] Ralph | Spin transfer torques[END_REF]. À cet égard, le graphène est un candidat attrayant, en raison de sa grande mobilité électronique ainsi que de son faible couplage spin-orbite intrinsèque, impliquant une grande longueur de cohérence de spin [START_REF] Tombros | Electronic spin transport and spin precession in single graphene layers at room temperature[END_REF][START_REF] Nouchi | Robustness of Spin Polarization in Graphene-Based Spin Valves[END_REF]. Certains résultats ont déjà été publiés [START_REF] Tombros | Electronic spin transport and spin precession in single graphene layers at room temperature[END_REF][START_REF] Dlubak | Highly efficient spin transport in epitaxial graphene on sic[END_REF], confirmant le potentiel du graphène pour le transport du signal de spin à température ambiante sur plusieurs dizaines de micromètres, ce qui est amplement suffisant pour des applications pratiques. Cependant, l'utilisation du graphène dans les éléments actifs de dispositifs spintroniques, tels que les transistors à effet de champ de spin (et pas uniquement comme conducteurs de courant de spin), nécessite la polarisation en spin de sa bande π.

Cela représente un véritable défi, car les spins des électrons ne subissent pratiquement aucun couplage avec leur mouvement dans le graphène (toute la structure de la bande est dégénérée en spin). Une façon d'induire une telle modification dans la dispersion électronique du graphène consiste à l'interfacer avec d'autres matériaux aux propriétés souhaitées. Ces interfaces avec le graphène, appelées systèmes hybrides, ouvrent la possibilité de concevoir la structure de bande du graphène grâce à de nouvelles propriétés électroniques.

Cette thèse se concentre sur la modification du cône de Dirac du graphène dans de tels systèmes hybrides e sa polarisation en spin. Dans cette perspective, deux interactions sont considérées : l'interaction d'échange et le couplage spin-orbite.

Il a été récemment démontré que les atomes de carbone d'une couche de graphène interfacé avec un matériau ferromagnétique présentent un moment magnétique d'environ 0.1 µ B [START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF], dû à une hybridation forte entre le graphène et le matériau ferromagnétique. Cependant, cette hybridation détruit le cône de Dirac du graphène au niveau de Fermi. Si cette hybridation est réduite, on peut espérer provoquer une interaction Dans le chapitre 2, une étude bibliographique de l'état de l'art de l'ingénierie de bande du graphène est présentée. Une première partie se focalise sur le graphène et le fort intérêt qu'il a suscité dans les dernières décennies. Ses propriétés mécaniques, thermiques et chimiques sont brièvement présentées ainsi que ses applications. L'accent est ensuite mis sur les propriétés électroniques exceptionnelles du graphène, et notamment sur l'origine de la dispersion linéaire de sa bande π. Un modèle de liaisons fortes est construit, d'abord juqu'aux plus proches voisins, puis jusqu'aux troisièmes plus proches voisins, permettant de décrire la dispersion électronique du graphène au voisinage du point K de sa zone de Brillouin. Ce modèle sera par la suite utilisé pour caractériser la modification de la dispersion de la bande π du graphène. L'état de l'art de l'ingénierie de bande du graphène est alors présenté de manière nonexhaustive, se focalisant sur trois propriétés induites dans le graphène : l'ouverture d'une bande d'énergie interdite, l'induction de couplage spin-orbite, et l'interaction d'échange.

L'ouverture d'une bande d'énergie interdite dans la structure de bande du graphène est nécessaire pour son application dans des dispositifs logiques et/ou nanoélectroniques.

Deux mécanismes permettant d'induire cette propriété sont expliqués : l'hybridation des états électroniques aux points K de la zone de Brillouin, et la rupture de l'équivalence entre les deux sous-réseaux atomiques A et B du graphène. Ce dernier peut être réalisé par l'interaction du graphène avec un substrat adéquat, et est illustré par plusieurs exemples [START_REF] First | Substrate-induced bandgap opening in epitaxial graphene[END_REF][START_REF] Wang | Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride[END_REF][START_REF] Varykhalov | Effect of noble-metal contacts on doping and band gap of graphene[END_REF]. Les valeurs maximales de la bande d'énergie interdite obtenues jusqu'à aujourd'hui sont présentées et les données expérimentales de spectroscopie photoélectrique correspondantes sont montrées.

Concernant le couplage spin-orbite, le rôle prometteur du graphène dans le domaine de la spintronique est rappelé. L'origine du couplage spin-orbite est expliquée, différenciant le couplage spin-orbite intrinsèque et extrinsèque (aussi appelé Rashba). Cette interaction est ensuite appliquée à la dispersion électronique particulière du graphène, ajoutant un terme à l'hamiltonien effectif, et son effet sur la structure de bande est discuté. La texture de spin résultante du cône de Dirac est illustrée : le cône de Dirac est divisé en deux sous-bandes polarisées en spin, le spin pouvant changer dans une même bande (fig.

2.9). Dans un second temps, les réalisations expérimentales et les simulations théoriques de systèmes induisant un couplage spin-orbite dans le graphène sont cités [START_REF] Wu | Spin-orbit splitting in graphene on metallic substrates[END_REF][START_REF] Klimovskikh | Nontrivial spin structure of graphene on Pt(111) at the Fermi level due to spin-dependent hybridization[END_REF][START_REF] Marchenko | Spin splitting of Dirac fermions in aligned and rotated graphene on Ir(111)[END_REF]. L'induction du couplage spin-orbite dans la structure de bande du graphène a, jusqu'à Résumé en francais x présent, été majoritairement obtenue par l'hybridation du graphène avec des métaux lourds (numéro atomique élevé) tels que l'or, le plomb ou le platine. Une valeur record de la séparation en énergie due au couplage spin-orbite d'environ 100 meV a été obtenue par l'intercalation d'une monocouche d'or entre le graphène et son substrat Ni [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] [START_REF] Marchenko | Graphene for spintronics: giant Rashba splitting due to hybridization with Au[END_REF].

L'origine de ce couplage, intrinsèque ou extrinsèque, est encore débattu. L'interaction d'échange peut être induite dans la dispersion électronique du graphène par hybridation avec un matériau ferromagnétique, et plusieurs exemples de matériaux ferromagnétiques isolants ou antiferromagnétiques sont cités [START_REF] Su | Effect of intervalley interaction on band topology of commensurate graphene/EuO heterostructures[END_REF][START_REF] Heiman | Strong interfacial exchange field in the graphene/EuS heterostructure[END_REF][START_REF] Leutenantsmeyer | Proximity induced room temperature ferromagnetism in graphene probed with spin currents[END_REF][START_REF] Ren | Magnetic proximity effect in graphene coupled to a BiFeO3 nanoplate[END_REF]. Nous nous concentrons ensuite sur les métaux ferromagnétiques, fer (Fe), nickel (Ni) et cobalt (Co).

Grâce au faible décalage de leur paramètre de maille par rapport à celui du graphène, les surfaces Ni [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] et Co(0001) recouvertes d'une couche de graphène ont été étudiées [START_REF] Trauzettel | Intact Dirac Cones at Broken Sublattice Symmetry: Photoemission Study of Graphene on Ni and Co[END_REF][START_REF] Varykhalov | Electronic and Magnetic Properties of Quasifreestanding Graphene on Ni[END_REF], et une forte interaction avec le graphène a été mesurée. La dispersion électronique d'un tel système montre la destruction du cône de Dirac au niveau de Fermi et un décalage de la bande π en énergie d'environ 2.5 -3 eV. L'origine de cette forte modification de la structure de bande est encore débattue.

Nous nous intéressons ensuite à la croissance du graphène sur un substrat. La nécessité d'un environnement ultra-vide est soulignée pour obtenir un graphène d'une grande qualité cristalline. Dans un tel environnement, deux techniques de croissance sont expliquées : la ségrégation et le dépôt chimique en phase vapeur (en anglais, chemical vapor deposition, CVD). Pour la première, le chauffage du substrat à de hautes températures permet aux atomes de carbone dissous dans le matériau de remonter à la surface et de s'organiser en une couche de graphène. La seconde utilise une source extérieure de carbone sous la forme d'un gaz de molécules d'hydrocarbure (souvent de l'éthylène), qui, en contact avec le substrat chaud, se dissocient et permettent la croissance du graphène. De nombreux exemples de substrat sont donnés [START_REF] Ago | Epitaxial chemical vapor deposition growth of single-layer graphene over cobalt film crystallized on sapphire[END_REF][START_REF] Loginova | Factors influencing graphene growth on metal surfaces[END_REF][START_REF] Sasaki | Moiré contrast in the local tunneling barrier height images of monolayer graphite on Pt(111)[END_REF][START_REF] Losurdo | Graphene CVD growth on copper and nickel: Role of hydrogen in kinetics and structure[END_REF][START_REF] Castner | LEED and thermal desorption studies of small molecules[END_REF]. La couche de graphène n'ayant pas exactement les mêmes paramètres de maille que le substrat, une super-périodicité de la couche de graphène est obtenue, formant un motif appelé moiré, qui est observable par microscopie à effet tunnel. Dans ce travail, nous avons choisi un substrat d'iridium Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] pour sa faible interaction avec le graphène et pour la croissance autolimitée du graphène sur celui-ci. La croissance et la structure du système Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] a déjà été longuement étudiée [START_REF] Michely | Growth temperature dependent graphene alignment on Ir(111)[END_REF][START_REF] Coraux | Structural coherency of graphene on Ir(111)[END_REF][START_REF] N'diaye | Selecting a single orientation for millimeter sized graphene sheets[END_REF], permettant d'obtenir une couche de graphène de grande qualité cristalline, avec une seule orientation. Une surface d'Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] partiellement recouverte de graphène peut aussi être obtenue par la méthode de croissance programmée en Résumé en francais xi température (en anglais, temperature-programmed growth, TPG). La surface du substrat est saturée de molécules d'hydrocarbures (éthylène dans notre cas) à température ambiante. Le substrat est ensuite chauffé très rapidement à haute température ( 1500 K), permettant la création de nombreux sites de nucléation du graphène et la croissance de nombreux domaines monocristallins de graphène (appelés feuillets). La répétition de ce cycle permet d'ajuster la proportion de la surface recouverte par le graphène. On obtient ainsi le système Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF].

Comme toutes les méthodes de croissance du graphène nécessite une haute température à laquelle une monocouche métallique ne résisterait pas (désorption, formation d'alliage, dissolution dans le substrat), la meilleure façon d'interfacer une telle monocouche est l'intercalation. De nombreuses espèces ont déjà été intercalées sous une couche de graphène [START_REF] Lacovig | Key role of rotated domains in oxygen intercalation at graphene on Ni(111)[END_REF][START_REF] Voloshina | Restoring a nearly free-standing character of graphene on Ru(0001) by oxygen intercalation[END_REF][START_REF] Halle | Filling the Gap: Li-Intercalated Graphene on Ir(111)[END_REF][START_REF] Sandin | Multiple coexisting intercalation structures of sodium in epitaxial graphene-SiC interfaces[END_REF][START_REF] Hofmann | Sequential oxygen and alkali intercalation of epitaxial graphene on Ir(111): enhanced many-body effects and formation of pn -interfaces[END_REF], mais l'intercalation de palladium n'a pas beaucoup été étudiée. Nous nous limitons donc à l'intercalation du cobalt, plus étudiée. Déposé à température ambiante, le cobalt forme des amas à la surface de Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. En chauffant alors l'échantillon, les atomes cobalt migrent et s'intercalent entre le graphène et l'iridium, par deux mécanismes : soit les atomes de cobalt passent à travers la couche de graphène par des défauts ou sur les bords de marches atomiques du substrat (intercalation "par dessus"), soit ils s'intercalent à travers les bords des feuillets de graphène (intercalation "par le côté"). Un alliage de surface entre le cobalt et l'iridium commence à se former à 770 K [START_REF] Drnec | Surface alloying upon Co intercalation between graphene and Ir(111)[END_REF], limitant la fenêtre de température possible pour l'intercalation (et donc la mobilité des atomes de cobalt). Étant limité en température, deux stratégies sont possibles pour optimiser l'intercalation du cobalt : augmenter la densité de défauts de la couche de graphène pour l'intercalation "par dessus" ou augmenter le nombre de bords de feuillets de graphène pour l'intercalation "par le côté". Dans le chapitre 4, les deux stratégies sont testées pour finalement obtenir un compromis : la croissance par TPG du graphène avec une grande densité de bords de feuillet, et le dépôt à chaud (400 • C, en-dessous de la température de formation de l'alliage Co-Ir) de Co (ou Pd) pour éviter la formation d'amas.

Après cette étude bibliographique de l'ingénierie de bande du graphène et de sa croissance, le chapitre 3 présente les deux méthodes expérimentales principalement utilisées dans ce travail : la microscopie à effet tunnel (en anglais, scanning tunneling microscopy, STM) et la spectroscopie photoélectronique résolue en angle (en anglais, angle-resolved Résumé en francais xii photoemission spectroscopy, ARPES).

La première, inventée en 1981 [START_REF] Binnig | Surface studies by scanning tunneling microscopy[END_REF], permet d'obtenir des informations sur l'organisation et la structure électronique de la surface d'un échantillon, à une échelle très locale (subnanométrique). Les principes de base de cette technique sont rappelés. Lorsqu'une pointe conductrice est très proche d'une surface conductrice (≈ 5 -10 Å), les électrons peuvent traverser le vide entre les deux par effet tunnel. Lorsqu'une tension est appliquée entre la pointe et l'échantillon, un courant est obtenu, appelé courant tunnel, qui est fonction du recouvrement des fonctions d'onde électroniques de la pointe et de l'échantillon, de leurs densités d'états locale et de la tension. Cette technique permet de réaliser des mesures topographiques et spectroscopiques. Dans ce travail nous avons réalisé uniquement des mesures topographiques par STM. Pour cela, on utilise le mode dit de "courant constant". Le courant de consigne est fixé à une valeur I 0 , et un système d'asservissement convertit les variations de courant en variation de la distance surface-pointe (z), via des transducteurs piézoélectriques. Le signal est enregistré en fonction de la position (x, y) de la surface, obtenant ansi une carte z(x, y) de la surface.

Ce phénomène est détaillé et mis en équation. On peut alors remarquer que le signal mesuré, pour des mesures topographiques, n'est pas uniquement relié à la topographie de la surface, mais également à sa densité d'états locale.

La spectroscopie photoélectronique résolue en angle (ARPES) permet de mesurer les états électroniques occupés. Un faisceau de photons d'énergie hν (plus grande que le travail de sortie des électrons) est envoyé sur l'échantillon, et des électrons sont alors émis (appelés photoélectrons) avec une énergie cinétique E cin . Selon l'énergie incidente des photons, on peut distinguer deux types de spectroscopie photoélectronique : la photoémission dans l'ultra-violet (en anglais, ultra-violet photoemission spectroscopy, UPS) avec hν < 100 eV permettant de sonder les bandes de valence, que nous utilisons dans ce travail, et la photoémission des rayons X (en anglais, X-rays photoemission spectroscopy, XPS) avec hν = 0.1-10 keV, permettant de sonder les états de coeur. Le phénomène est ensuite détaillé et mis en équation dans un modèle à trois étapes : l'excitation optique, le transfert à la surface, et le passage au travers de la surface. Lors de cette description, la relation entre le vecteur d'onde des photoélectrons et leur énergie cinétique est précisée.

Par la suite, les différentes parties de notre dispositif expérimental sont alors présentées : la chambre ultra-vide, la source de photons, le goniomètre, le cryostat et l'analyseur.

Les mesures sont effectuées dans un vide de 3.10 -10 mbars. La lampe à décharge dans l'hélium gazeux, suivie d'un monochromateur/polariseur, nous permet d'obtenir

Résumé en francais xiii des photons ayant deux énergies possibles, 21.22 eV (HeI) ou 40.81 eV (HeII), polarisés à 90% (polarisation s ou p). Le goniomètre, placé devant le faisceau de photons, permet le mouvement de l'échantillon selon trois translations (x, y, z) et trois rotations (θ, φ, ψ).

La correspondance entre ces angles de mesure et la région mesurée de l'espace réciproque est détaillée dans l'annexe A. La zone de l'espace réciproque que nous étudions dans ce travail se trouve au voisinage du point K du graphène (K Gr ) et du point K du substrat L'intercalation de cobalt à 400 • C sous une couche complète de graphène (préalablement réalisée par dépôt chimique en phase vapeur à 1100 • C) est ensuite étudiée. L'amplitude du motif caractéristique moiré des régions intercalées est bien plus grande que celle de la simple couche de graphène (95 pm contre 10 pm), confirmant l'interaction forte entre le graphène et la couche de cobalt. Nous montrons que l'intercalation du cobalt reste très limitée, avec une petite proportion de la quantité déposée qui s'intercale, alors que la majorité restante forme des amas à la surface du graphène. L'augmentation de la température à 500 Le chapitre 8 présente les conclusions et les perspectives de cette thèse.

Cette thèse représente un premier pas vers l'étude des propriétés électroniques des systèmes hybrides graphène/métal où la structure de la couche métallique peut être contrôlée à l'échelle nanométrique. Jusqu'à présent, l'accent a été mis sur l'interaction du graphène avec des monocouches atomiques composées d'un ou deux éléments. À cet égard, plusieurs aspects restent encore à étudier. Chapter 1

Introduction

In the last few decades the study of the physical and chemical properties of lowdimensional systems has rose due to an extraordinary and steep technological advance.

For the first time it has been possible to study and engineer structures down to the atomic level where fascinating phenomena take place. It has been demonstrated that, often, the reduction of dimensionality and size results in completely new mechanical [START_REF] Tolbert | High-pressure structural transformations in semiconductor nanocrystals[END_REF][START_REF] Wong | Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes[END_REF][START_REF] Akinwande | A review on mechanics and mechanical properties of 2d materials-graphene and beyond[END_REF], optical [START_REF] Wilcoxon | Photoluminescence from nanosize gold clusters[END_REF][START_REF] Yao | Large optical activity of gold nanocluster enantiomers induced by a pair of optically active penicillamines[END_REF], electronic [START_REF] Shipway | Nanoparticle arrays on surfaces for electronic, optical, and sensor applications[END_REF][START_REF] Gittins | A nanometre-scale electronic switch consisting of a metal cluster and redox-addressable groups[END_REF], and magnetic [START_REF] Leslie-Pelecky | Magnetic properties of nanostructured materials[END_REF][START_REF] Gambardella | Giant magnetic anisotropy of single cobalt atoms and nanoparticles[END_REF] properties of the material.

This makes nanoscience and nanotechnology among the most important research fields for both fundamental and applicative perspectives.

Among all the different research fields on low dimensional systems, scientific research on graphene (Gr) has been particularly active. The appeal for such material comes from the wide range of possible applications [START_REF] Chung | Biomedical applications of graphene and graphene oxide[END_REF][START_REF] Huang | An overview of the applications of graphenebased materials in supercapacitors[END_REF][START_REF] Perreault | Environmental applications of graphene-based nanomaterials[END_REF][START_REF] Bae | Towards industrial applications of graphene electrodes[END_REF][START_REF] Palacios | Applications of graphene devices in rf communications[END_REF] originating from both its oustanding mechanical [START_REF] Bizao | Mechanical properties of graphene nanowiggles[END_REF][START_REF] Lee | Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene[END_REF] and electronic properties [START_REF] Novoselov | The electronic properties of graphene[END_REF][START_REF] Geim | The rise of graphene[END_REF][START_REF] Geim | Graphene : Status and Prospects[END_REF]. Gr, a two-dimensional allotrope of carbon, indeed exhibits an exceptionally high electron mobility, originating from a linear dispersion of its π band, called Dirac cone. The electrons velocity in Gr is about 150 times higher than in silicium, which is expected to result in significant enhancement of new generation electronic devices performances. Besides, Gr is made of carbon, a cheap and abundant material, offering an ecological and economical alternative to the current technology. However, in order to use graphene in fully developed devices, modifications of its electronic properties, such as a gap induction or spin-polarization, are necessary. This requirement has made the band engineering of graphene a very active field of research in the last 15 years.

Considering the applications of low dimensional systems, one of the most appealing is spintronics, which aims to use the spin degree of freedom of electrons for new forms of information storage and logic devices. The foundational step of spintronics was the discovery of giant magneto-resistance in thin-films structures [START_REF] Baibich | Giant magnetoresistance of (001) fe/(001) cr magnetic superlattices[END_REF][START_REF] Binasch | Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange[END_REF] and has resulted in a massive technological impact in magnetic field sensors, which are currently used in hard disk drives, biosensors, microelectromechanical systems (MEMS) and magnetoresistive random-access memories (MRAM). The field of spintronics experiences a second revolution after the discovery of the spin transfer torque effect (STT), which permits the control of the magnetization with electrical current [START_REF] Myers | Currentinduced switching of domains in magnetic multilayer devices[END_REF][START_REF] Berger | Emission of spin waves by a magnetic multilayer traversed by a current[END_REF][START_REF] Ralph | Spin transfer torques[END_REF]. In this regard, graphene is an appealing candidate, owing to its high carrier mobility together with its weak intrinsic spin-orbit coupling (SOC), implying a long spin-coherence length [START_REF] Tombros | Electronic spin transport and spin precession in single graphene layers at room temperature[END_REF][START_REF] Nouchi | Robustness of Spin Polarization in Graphene-Based Spin Valves[END_REF].

Some results have already been published [START_REF] Tombros | Electronic spin transport and spin precession in single graphene layers at room temperature[END_REF][START_REF] Dlubak | Highly efficient spin transport in epitaxial graphene on sic[END_REF], confirming the potential of graphene for transporting spin signal at room temperature (RT) over tens of micrometers, which is more than enough for practical applications of lateral spintronics. However, using graphene in active elements of spintronics devices, such as spin field-effect transistor (not only as high efficiency spin current leads), requires the spin-polarization of its π band. This represents a real challenge, since electron spins experience almost no coupling with electron motion in graphene (its entire band structure is spin-degenerate).

One way to induce such a modification in the graphene electronic dispersion is to interface it with other materials with desired properties. These graphene interfaces, called

hybrid systems, open the possibility to engineer the graphene band structure by inducing novel properties.

The present work is focused on inducing a spin-polarization of the Dirac cone of graphene in such hybrid systems. In this perspective, two interactions are considered: exchange interaction and spin-orbit coupling. It has recently been shown that carbon atoms of a graphene layer interfaced with a ferromagnetic material (FM) present a magnetic moment of about 0.1 µ B [START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF], caused by the strong hybridization between graphene and the FM. However, this hybridization is destroying the Dirac cone of graphene at the Fermi level. If this hybridization is lowered, one can hope to induce exchange interaction in graphene while conserving its linear electronic dispersion. In this work, we concentrate on the interface between graphene and one monolayer (ML) of cobalt (Co) and between a CoIr alloy. The alloy can be used to tune the average strength of the interaction while preserving the global magnetization of the system.

Regarding SOC, so far, heavy metals (high atomic number) have been interfaced with graphene to induce SOC in its band structure. A maximal value of spin-orbit splitting of 100 meV has been achieved in graphene by interfacing it with one ML of gold [START_REF] Marchenko | Graphene for spintronics: giant Rashba splitting due to hybridization with Au[END_REF].

However, these heavy materials, which possess a high intrinsic SOC, have normally a weak interaction with graphene [START_REF] Vanin | Graphene on metals: A Van Der Waals density functional study[END_REF][START_REF] Voloshina | Realistic Large-Scale Modeling of Rashba and Induced Spin -Orbit Effects in Graphene / High-Z-Metal Systems[END_REF]. In this work, our strategy is to enhance the interaction of a strong SOC material with graphene. In this regard, palladium (Pd) is a good candidate, since it has an intermediate binding energy with graphene (higher than gold, lower than Co to prevent the destruction of the Dirac cone) and an intermediate intrinsic SOC.

The study presented in this thesis is focused on the interaction between graphene and single atomic layers. Such hybrid systems allow to access a new parameter for the band engineering: the layer lattice constant. As it will be presented in the following, graphene will be first grown on an Ir(111) substrate, the metallic monolayer will then be intercalated between graphene and Ir [START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF][START_REF] Pacilé | Artificially lattice-mismatched graphene/metal interface: Graphene/Ni/Ir(111)[END_REF]. In such a situation, the intercalant will grow pseudomorphic to the Ir, i.e. it will acquire the Ir lattice constant [START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF][START_REF] Drnec | Surface alloying upon Co intercalation between graphene and Ir(111)[END_REF].

Increasing the number of intercalated atomic layers results in the relaxation of the metallic film [START_REF] Drnec | Surface alloying upon Co intercalation between graphene and Ir(111)[END_REF][START_REF] Carlomagno | Co film stretching induced by lattice mismatch and annealing: The role of graphene[END_REF]. Therefore, with such procedure, the registry between graphene and its substrate can be tuned becoming a new parameter for band engineering. Of course, this requires several years of experiments in order to find the right growth conditions of the sample. For this reason, in this thesis work, we focus on intercalated single atomic layer which represents the starting point of such study.

The structure of this work is detailed as follows.

Chapter 2 presents an overview of the scientific work realized on the graphene band engineering. A first part is briefly developing the exceptional properties of graphene, focusing on its electronic dispersion. A tight-binding model is developed up to the thirdnearest neighbor, and will be used in following chapters.

The state of the art of graphene band engineering is then presented. Three main electronic features are discussed: band gap opening, spin-orbit coupling and exchange interaction. For each one of them, the phenomenon is explained with the help of recent scientific publications.

The growth of high-quality graphene on different substrates is then presented. Several growth techniques in an ultra-high vacuum (UHV) environment are developed and the structures of the resulting graphene layer are discussed. A final part focuses on the growth of Gr on the Ir(111) substrate, comparing two growth methods which enable tailoring the graphene layer while keeping a high crystalline quality.

Since the growth of high-quality graphene requires high temperature (>1400 K), interfacing a metallic monolayer with it must be done after the graphene growth. This implies that the Co or Pd layer has to be intercalated between Gr and Ir. Since the Pd intercalation has not yet been extensively addressed by the scientific community, the last part of this chapter will briefly address the intercalation of Co under graphene. We first present an attempt of the intercalation "from the top" of Co under a complete graphene layer. The amount of intercalated Co remains very low up to an annealing temperature of 500 • C, at which a surface alloy between Co and Ir starts to form.

We then employed an alternative growth method for graphene, called temperatureprogramed growth (TPG), which allows to control the surface coverage of the graphene layer and its flake edges density.

The intercalation "from the side" of the graphene flakes of Pd and Co under graphene with a high density of flake edges is then presented, demonstrating the complete intercalation of both materials.

A comparative ARPES study of several TPG-grown graphene layers with respect to a complete graphene layer is done, confirming that our TPG-grown graphene is a viable option for ARPES measurements.

Chapter 5 presents the spectroscopic study of Gr/Co hybrid systems.

After a brief presentation of the state of the art, the band structure of each component of the hybrid system is identified. The electronic properties of our TPG-grown Gr/Co hybrid are compared with the one grown by the typical method used in literature. We demonstrate that, altough the Dirac cone is destroyed in both cases, with our growth strategy the band structure of the hybrid is better defined.

Finally, the effect of the Co-Ir surface alloying on the graphene band structure is discussed. The rise of the annealing temperature above the alloy formation temperature results in a strong modification of the graphene Dirac cone with an enhancement of the electrons velocity.

Chapter 6 presents the spectroscopic study of Gr/Pd hybrid systems.

After a brief presentation of the state of the art, the band structure of each component of the hybrid system is identified. We show that, upon the intercalation of one ML of Pd between Gr and Ir, SOC is induced in graphene band structure by hybridization of its π band with spin-polarized quantum well states of the Pd monolayer on the Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] substrate. Our experimental data are supported by density functional theory (DFT) calculations.

Chapter 7 presents the preliminary results on the co-intercalation of Co and Pd between Gr and Ir. STM measurements of successive intercalation of Co and Pd are shown, with ARPES measurements of Pd Rich, Gr/CoPd hybrids. We show that the induced SOC in graphene by Pd intercalatation is preserved with the appearance of new, linearly dispersing electronic states at the Fermi level.

In Chapter 8, the main results are summarized together with some routes for future research.

Chapter 2

Graphene band engineering

This chapter will first introduce graphene, address its outstanding properties and explain the great interest it raised in the last decade. This thesis work is focused on graphene band engineering, therefore we will propose a non-exhaustive overview of modifications of the graphene electronic properties. The last two parts will address the growth and structural properties of graphene and graphene/intercalant hybrid systems.

Graphene

Graphene has been theoretically explored since 1947 [START_REF] Wallace | The band theory of graphite[END_REF] and many studies have been performed in the next few decades on few-layer graphite [START_REF] Boehm | Surface Properties Of Extremely Thin Graphite Lamealle[END_REF]. Starting in the 70's, single layers of epitaxial graphene have been grown and studied on many different substrates [START_REF] Chuhei | Ultra-thin epitaxial films of graphite and hexagonal boron nitride on solid surfaces[END_REF] but significant charge transfers from the substrate was altering its band structure.

It is only in 2004 that Geim and Novoselov (Nobel Prize 2010) extracted a single layer of graphene onto thin silicon dioxide from bulk graphite by the so-called "scotch tape" technique [START_REF] Novoselov | Electric field effect in atomically thin carbon films[END_REF] and proved by further experiments (observation of the predicted half-integer quantum Hall effect and relativistic Dirac electronic transport properties) the existence of graphene [START_REF] Zhang | Experimental observation of the quantum Hall effect and Berry's phase in graphene[END_REF][START_REF] Dubonos | Two-dimensional gas of massless Dirac fermions in graphene[END_REF]. Since then, graphene has been extensively studied worldwide. This section will address graphene properties and explain the reasons of such a great interest.

In a second part, its peculiar electronic band structure will be addressed with the help of a simple tight-binding model.

Graphene outstanding properties

Graphene, a two-dimensional allotrope of carbon, plays a key role since it is the basis for the understanding of the properties in other carbon allotropes. Graphene is made out of carbon atoms separated by 1.42 Å arranged on a honeycomb lattice.

It exhibits outstanding mechanical and thermal properties. It has been indeed experimentally characterized by a Young modulus of 1 TPa, a third-order stiffness of D = -2

TPa and a record value of its intrinsic strength of σ int = 130 GPa [START_REF] Bizao | Mechanical properties of graphene nanowiggles[END_REF][START_REF] Lee | Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene[END_REF], values confirmed by simulations [START_REF] Liu | Ab initio calculation of ideal strength and phonon instability of graphene under tension[END_REF], which makes graphene the "strongest material in the universe". As a comparison, steel usually used for construction has a Young modulus of the order of 200 GPa. An other record value for room-temperature thermal conductivity of 5000 W m -1 K -1 has also been recorded [START_REF] Balandin | Thermal properties of graphene and nanostructured carbon materials[END_REF]. Graphene can be stretched elastically by as much as 20%, more than any other crystal [START_REF] Lee | Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene[END_REF]. Also, it exhibits simultaneously high pliability (folds and pleats are commonly observed) and brittleness (it fractures like glass at high strains) [START_REF] Bangert | Macroscopic Graphene Membranes and Their Extraordinary Stiffness[END_REF]. Equally unprecedented is the observation that the one-atomthick film is impermeable to gases, including helium [START_REF] Mceuen | Impermeable Atomic Membranes from Graphene Sheets[END_REF], which makes graphene the "world's thinnest balloon". An other important aspect of graphene is its chemical reactivity. It can indeed adsorb and desorb various atoms and molecules, retrieving easily its original state by thermal annealing or chemical treatment. Its chemical functionalization opens a huge field of possible applications by creating new 2D materials with a wide range of mechanical and electronic properties [START_REF] Chua | Covalent chemistry on graphene[END_REF][START_REF] Gao | Graphene Oxide: Reduction Recipes, Spectroscopy, and Applications[END_REF][START_REF] Liao | Chemistry makes graphene beyond graphene[END_REF]. Graphene has also been used in composites materials like polymers to enhance their mechanical properties [START_REF] May | Approaching the theoretical limit for reinforcing polymers with graphene[END_REF]. All these mechanical, thermal and chemical properties make graphene a promising material for a wide range of applications but one of the main reason for the rising interest for graphene is its outstanding electronic properties.

The sp 2 hybridization between one s orbital and two p orbitals of carbon atoms leads to a trigonal planar structure with a formation of a σ bond (separated by 1.42 Å).

This σ band is responsible for the robustness of the lattice structure in all allotropes.

The unaffected p z orbital, which is perpendicular to the planar structure, can bind covalently with neighboring carbon atoms, leading to the formation of a half-filled π band. The "outstanding" electronic properties of graphene originate from its low-energy band structure at six particular points of its Brillouin zone (BZ) schematized in fig.

H = v F σ. κ (2.1)
, where σ is the 2D Pauli matrix. Electronic states near Fermi level are composed of states belonging to the different sublattices and their relative contributions have to be taken into account by introducing an index for each of the sublattice, which is similar to the spin index (up and down), and, therefore, is referred to as "pseudospin". This pseudospin is the origin of the chirality in graphene. Graphene can also be considered as a zero-gap semiconductor, since its density of states is zero at the Fermi level. That makes graphene a very practical semiconductor because its Fermi level can easily be shifted in energy by applying a gate voltage and since there is no gap, it allows a precise tuning of its density of states. This peculiar band structure leads to several quantum effects such as half-integer quantum Hall effect or Klein tunneling, which have been extensively measured and reviewed [START_REF] Novoselov | The electronic properties of graphene[END_REF][START_REF] Geim | The rise of graphene[END_REF][START_REF] Geim | Graphene : Status and Prospects[END_REF].

In the next part, we will explain in more details the graphene band structure, more precisely its calculation from a tight-binding model. This model will then be used in the following experimental parts of this work.

Graphene band structure: tight-binding model

The first tight-binding description of graphene was given in 1947 by Wallace [START_REF] Wallace | The band theory of graphite[END_REF]. He considered nearest-and next-nearest neighbor interaction for the graphene p z orbitals, but neglected the overlap between wave functions centered at different atoms. A second tight-binding approximation was nicely described in [START_REF] Dresselhaus | Physical properties of carbon nanotubes[END_REF]: it considers the nonfinite overlap between the basis functions, but includes only interactions between nearest neighbors within the graphene sheet. In this work, we start from the most general form of the secular equation, with H the tight-binding hamiltonian, S the overlap matrix and A and B the two carbon sublattices [START_REF] Reich | Tight-binding description of graphene[END_REF]:

H AA ( k) -E( k)S AA ( k) H AB ( k) -E( k)S AB ( k) H * AB ( k) -E( k)S * AB ( k) H AA ( k) -E( k)S AA ( k) = 0 (2.2)
, where E( k) are the electronic eigenvalues. Let's first derive the nearest-neighbor tightbinding dispersion. All nearest neighbors belong to the other sublattice and we obtain:

H AA = 1 N -→ R A ϕ A ( r - -→ R A )|H|ϕ A ( r - -→ R A ) (2.
3)

H AB = 1 N -→ R A -→ R B e i k( -→ R A - -→ R B ) ϕ A ( r - -→ R A )|H|ϕ B ( r - -→ R B ) (2.4) S AB = 1 N -→ R A -→ R B e i k( -→ R A - -→ R B ) ϕ A ( r - -→ R A )|ϕ B ( r - -→ R B ) (2.5)
, where N is the number of unit cells in the crystal, -→ R A and -→ R B are the positions of atom A and B and ϕ A and ϕ B denote the p z atomic wave function forming the basis for the crystal Bloch functions. We now define:

f ( k) = 3 + 2 cos 2πak 1 + 2 cos 2πak 2 + 2 cos 2πa(k 1 -k 2 ) (2.6) ε 2p = 1 N -→ R A ϕ A ( r - -→ R A )|H|ϕ A ( r - -→ R A ) (2.7) γ 0 = ϕ A ( r - -→ R A )|H|ϕ B ( r - -→ R A - -→ R 1i ) (2.8
)

s 0 = ϕ A ( r - -→ R A )|ϕ B ( r - -→ R A - -→ R 1i ) (2.9)
, with -→ R 1i (i=1,2,3) the vector pointing from atom A 0 to atoms B 1i in fig. 2.2, which gives:

H AA = ε 2p (2.10a
)

H AB = γ 0 (e i k. --→ R 11 + e i k. --→ R 12 + e i k. --→ R 13 ) (2.10b) S AB = s 0 (e i k. --→ R 11 + e i k. --→ R 12 + e i k. --→ R 13 ) (2.10c)
, and by substituting 2.10 in 2.2, we finally obtain for the dispersion relation:

E ± ( k) = ε 2p ∓ γ 0 f ( k) 1 ∓ s 0 f ( k) (2.11)
The three parameters ε 2p , γ 0 and s 0 are found by fitting experimental or first-principles data for freestanding graphene. The typical values obtained are ε 2p = 0 eV, γ 0 between -2.5 and -3 eV and s 0 below 0.1. This first nearest neighbor dispersion is in good agreement with first-principle calculation only in a small momentum and energy range around the K point of the BZ, as shown in fig. 2.3a).

We now extend the tight-binding model to the second and third nearest neighbors, since

| -→ R 2i | = 2.461 Å is very close to | -→ R 3i | = 2.842 Å.
The general solution of equation 2.2 is:

E ± ( k) = -(-2E 0 + E 1 ) ± (-2E 0 + E 1 ) 2 -4E 2 E 3 2E 3 (2.12)
, with:

E 0 = H AA S AA (2.13
)

E 1 = S AB H * AB + H AB S * AB (2.14) E 2 = H 2 AA -H AB H * AB (2.
15)

E 3 = S 2 AA -S AB S * AB (2.16)
In the case of the third nearest neighbor, we obtain for these energies:

E 0 = (ε 2p + γ 1 u( k))(1 + s 1 u( k))
(2.17)

E 1 = 2s 0 γ 0 f ( k) + (s 0 γ 2 + s 2 γ 0 )g( k) + 2s 2 γ 2 f (2 k) (2.18) E 2 = (ε 2p + γ 1 u( k)) 2 -γ 2 0 f ( k) -γ 0 γ 2 g( k) -γ 2 2 f (2 k) (2.
19)

E 3 = (1 + s 1 u( k)) 2 -s 2 0 f ( k) -s 0 s 2 g( k) -s 2 2 f (2 k) (2.20)
, with f, u and g functions defined as:

u( k) = 2 cos k. a 1 + 2 cos k. a 2 + 2 cos k.( a 1 -a 2 ) (2.21) f ( k) = 3 + u( k) (2.22) g( k) = 2u( k) + u(2k 1 -k 2 , k 1 -2k 2 ) (2.23)
γ 1 and γ 2 are the interaction energies with the second and third neighbors, and s 1 and s 2 are the corresponding overlaps. We have now seven fit parameters which is sufficient to accurately reproduce the first-principles results along all the high-symmetry directions of the BZ (fig. 2.3b)). In the following, we will use these tight-binding models to fit our experimental data: the first nearest neighbor model will be referred to as 1NN-TB and the third-nearest neighbor as 3NN-TB. Since the 3NN-TB model requires seven adjustable parameters, it will be used only to fit electronic structures measured in a wide energy range below the Fermi level and far from the K Gr point.

Band engineering in graphene

Its outstanding electronic properties (high electron velocity, linear dispersion, chirality) make graphene a promising candidate for various fields of applications such as graphenebased electronics (transistors going beyond the Si-based technology), electric batteries, spintronics, superconducting physics or quantum information [START_REF] Geim | The rise of graphene[END_REF][START_REF] Geim | Graphene : Status and Prospects[END_REF]. However, in order to use graphene in fully developed devices, a modification of its electronic properties is necessary. This requirement has made band engineering of graphene a very active field of research in the last 15 years. We propose in this section an insight of some interesting electronic features for potential applications which have been induced in graphene. We will start with the long standing problem of band gap opening in graphene and we will continue with spin-orbit and exchange interactions which are the core of this thesis work.

Band gap opening

The lack of a finite band gap in graphene implies that the current can never be tuned off completely, which is a major obstacle for its use in logic or high speed switching nanoelectronic devices (transistors). The challenge is then to simultaneously induce a sizable band gap in graphene band structure in order to obtain a large on/off ratio and conserve the high charge carriers mobility. There are two ways to lift the degeneracy of the valence and conduction bands at the Dirac points: one is to hybridize the electronic states at K and K', which requires breaking of the translational symmetry, the other is to break the equivalence between the two sublattices A and B. Some promising ways to induce such electronic features are patterned graphene (nanoribbons) [START_REF] Dvorak | Bandgap opening by patterning graphene[END_REF], bilayer of graphene [START_REF] Zhang | Direct observation of a widely tunable bandgap in bilayer graphene[END_REF] or by applying shear strain [START_REF] Kerszberg | Ab initio strain engineering of graphene: Opening bandgaps up to 1 eV[END_REF][START_REF] Cocco | Gap opening in graphene by shear strain[END_REF]. All these methods go beyond a single monolayer of graphene and will not be further discussed. This work being about hybrid systems with a single monolayer of graphene, we will focus in this part on substrate- Gr/hBN (adapted from [START_REF] Wang | Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride[END_REF]), c) Gr/Cu(111) (adapted from [START_REF] Varykhalov | Effect of noble-metal contacts on doping and band gap of graphene[END_REF]) and d) Gr/Ag(111) (adapted from [START_REF] Varykhalov | Effect of noble-metal contacts on doping and band gap of graphene[END_REF]).

gap in graphene is hexagonal boron nitride (hBN) since it has the same honeycomb hexagonal lattice (stretched by 1.8%) and exhibits a wide band gap at K point of 6

eV. This band gap is due to the breaking of the inversion symmetry by distinct boron and nitrogen sublattices. By stacking graphene on top of hBN to form a Van der Waals heterostructure, a 160 meV gap at the K point has been observed [START_REF] Wang | Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride[END_REF] and calculated [START_REF] Fan | Band gap opening of graphene by doping small boron nitride domains[END_REF][START_REF] Shinde | Direct band gap opening in graphene by BN doping: Ab initio calculations[END_REF]. The same idea of breaking the two sublattices equivalence by substrate potential has been confirmed with other substrates such as SiC (band gap of 260 meV) [START_REF] First | Substrate-induced bandgap opening in epitaxial graphene[END_REF], P tSe 2 (band gap of 264 meV) [START_REF] Guan | Band gap opening of graphene by forming a graphene/PtSe2 van der Waals heterojunction[END_REF], Cu [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] (band gap of 180 meV) [START_REF] Varykhalov | Effect of noble-metal contacts on doping and band gap of graphene[END_REF] and Ag [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] (band gap of 320 meV) [START_REF] Varykhalov | Effect of noble-metal contacts on doping and band gap of graphene[END_REF]. Fig. 2.4 shows ARPES measurements at the Dirac point for some of these systems.

Breaking the equivalence of the two sublattices and, therefore, induce a band gap can also be achieved by adsorption or the intercalation of suitable elements. Large band gaps have been measured for such systems: 206 meV for adsorbed water molecules onto graphene [START_REF] Koratkar | Tunable Bandgap in Graphene by the Controlled Adsorption of Water Molecules[END_REF], 740 meV for Na/Ir/Gr [START_REF] Papagno | Large band gap opening between graphene Dirac cones induced by Na adsorption onto an Ir superlattice[END_REF] and 1 eV for hydrogenated graphene [START_REF] Farjam | Tunable Band Gap in Hydrogenated Quasi-Free-Standing Graphene[END_REF].

The large variety of molecules and elements which can be adsorbed on graphene offers a huge range of different interactions which could enable a precise tuning of the opened band gap [START_REF] Berashevich | Tunable band gap and magnetic ordering by adsorption of molecules on graphene[END_REF].

Spin-Orbit Coupling

Graphene in spintronics is predominantly considered for spin current leads of high performance [START_REF] Semenov | Spin field effect transistor with a graphene channel[END_REF] due to the weak intrinsic spin-orbit coupling of its π electrons, which, together with its high carrier mobilities, implies a long spin-coherence length [START_REF] Tombros | Electronic spin transport and spin precession in single graphene layers at room temperature[END_REF][START_REF] Nouchi | Robustness of Spin Polarization in Graphene-Based Spin Valves[END_REF].

Externally induced large SOC opens the possibility of using graphene in active elements of spintronics devices, such as spin field-effect transistor, through the spin-polarization of its Dirac cone. A real effort has been made these past few years to induce a large SOC in graphene while keeping its high carrier velocities. In this section, we will first introduce spin-orbit coupling and then present a quick overview of SOC induced in graphene.

Theory of spin-orbit coupling

The origin of spin-orbit coupling can first be explained by a classical point of view. When an electron with momentum p moves in a magnetic field B, it experiences a Lorentz force in the direction perpendicular to its motion F = -e p × B/m and possesses a Zeeman energy µ B σ. B, where σ is the vector of the Pauli spin matrices, m and e are the mass and charge of the electron, respectively, and µ B is the Bohr magneton. By analogy, when this electron moves in an electric field E, it experiences a magnetic field

--→ B ef f E × p/mc 2
in its rest-frame, a field that also induces a momentum-dependent Zeeman energy called the SO coupling, H SO µ B ( E× p). σ/mc 2 . The Zeeman interaction between the electron spin and this effective magnetic field is equivalent to the coupling of the electron spin and momentum degrees of freedom, known as SOC. SOC can split degenerate bands with finite angular momentum (p, d, f ), modifying the band structure.

The electric field inducing SOC can originate from the crystal potential (intrinsic SOC)

or from surfaces, interfaces or external applied electric field (extrinsic SOC). We will first focus our attention on intrinsic SOC.

In crystals, the electric field is given by the gradient of the crystal potential E = -∇V , which produces a SO field B( p) = -( ∇V × p)/mc 2 . The orbital dependence of the SOC strength is a key parameter. It is indeed well-known that the SOC strength λ increases rapidly with the atomic number Z. The spin-orbit interaction of an electron in a central field of potential V (r) is given [START_REF] Shanavas | Theoretical model for Rashba spin-orbit interaction in d electrons[END_REF] by:

H SO (r) = 1 2m 2 c 2 r ∂V (r) ∂r L. S (2.24)
Now if we are using the Coulomb potential V (r) = -Ze 2 r and the hydrogenic wave functions R nl (r), we obtain the well-known result:

λ nl = α 2 Z 4 n 3 l(l + 1/2)(l + 1) R y (2.25)
, which increases as Z 4 , with α being the fine-structure constant and R y the Rydberg constant. However, in the solid, the outer electrons are the relevant electrons, whose quantum numbers nl change with Z. If one considers the outermost electrons for the atoms without worrying about nl, then Landau and Lifshitz have argued that the spinorbit interaction strength should scale more like Z 2 :

λ = Aα 2 Z 2 R y (2.26)
, with A of the order of 1. This demonstrates the difficulty to induce SOC in graphene due to its low atomic number (Z C = 6).

As already mentioned, Gr is of great interest mostly because of its unique electronic properties originating from the gapless linear energy dispersion at the Fermi level, which makes the low-energy dynamics of electrons in this system equivalent to that of relativistic fermions, as described by the massless Dirac equation [START_REF] Semenoff | Condensed-Matter simulation of a three-Dimensional anomaly[END_REF]. However, this ideal picture changes qualitatively when SOC is taken into account. The cone-like dispersion of the π bands in the vicinity of the K (K') points of the Brillouin zone is described by the Dirac-type Hamiltonian:

H 0 = ε p -v F (τ σ x κ x + σ y κ y ) (2.27)
, with v F the Fermi velocity, κ the wave vector measured with respect to K (K'), σ Pauli matrices describing the so-called pseudospin space (σ z = 1 for sublattice A, σ z = -1 for sublattice B), and τ = 1(-1) for the cones K (K'). The eigenvalues of H 0 are given with respect to ε p , the energy of p orbitals. This Hamiltonian gives the usual linear dipersion of the so-called Dirac cones E ± ( κ) = ± v F | κ|. By now introducing SOC, we add a term in this Hamiltonian of the form [START_REF] Konschuh | Tight-binding theory of the spin-orbit coupling in graphene[END_REF]:

H ef f = H 0 + H I (2.28
)

H I = λ I τ σ z s z (2.29)
The exact effect of intrinsic spin-orbit coupling on graphene band structure is still debated and several theoretical works were recently published [START_REF] Voloshina | Realistic Large-Scale Modeling of Rashba and Induced Spin -Orbit Effects in Graphene / High-Z-Metal Systems[END_REF][START_REF] Kochan | Model spin-orbit coupling Hamiltonians for graphene systems[END_REF][START_REF] Frank | Theory of electronic and spin-orbit proximity effects in graphene on Cu (111)[END_REF][START_REF] Thakur | Spin-Orbit Coupling Induced Gap in Graphene on Pt(111) with Intercalated Pb Monolayer[END_REF] very small in graphene, from 1µeV to 25µeV according to different types of simulation [START_REF] Konschuh | Tight-binding theory of the spin-orbit coupling in graphene[END_REF][START_REF] Min | Intrinsic and Rashba spin-orbit interactions in graphene sheets[END_REF][START_REF] Yao | Spin-orbit gap of graphene: First-principles calculations[END_REF]. Therefore graphene is usually considered with no intrinsic SOC and a spin-degenerate Dirac cone. This situation can be dramatically changed by the use of interface effects. In fact, if graphene is interfaced with a material with intrinsic SO-split bands and the electronic hybridization is strong enough, a strong enhancement of λ I can be induced in the graphene layer providing a spin separation. Several examples will be given in the following sections.

An other way to induce SOC in a crystal is to broke its spatial inversion symmetry. It happens for example at the material surfaces and interfaces or when an external electric field is applied. This effect is called extrinsic SOC and more commonly called Rashba or Bychkov-Rashba SOC. Depending on the crystal symmetry, different SO Hamiltonians have been found. The first one was discovered by Dresselhaus [START_REF] Dresselhaus | Spin-orbit coupling effects in zinc blende structures[END_REF] in compounds lacking a center of inversion:

H D 3 = γ ((p 2 y -p 2 z )p x σ x + c.p.) (2.30)
, where c.p. denotes circular permutations of indices. Naturally, additional symmetries result in additional SOC terms, such as a strain along (001) direction going from the cubic Dresselhaus SOC given in 2.30 to the linear Dresselhaus SOC:

H D 1 = γp 2 z (p x σ x -p y σ y ) (2.31)
In quantum wells with inversion symmetry broken along the growth direction and respecting the C 2v symmetry, Bychkov and Rashba [START_REF] Bychkov | Properties of a 2d electron gas with lifted spectral degeneracy[END_REF] proposed phenomenologically that the interfacial electric field E = E z z results in a SOC of the form:

H R = α R ( z × p). σ (2.32)
, where α R is known as the Rashba parameter (also often called λ R or λ BR ). The spin texture at the Fermi surface in both Rashba and linear Dresselhaus SOC is shown in fig. 2.6. In both cases, SOC locks spin to the linear momentum and split the spin subbands in energy. Fig. 2.7 displays experimental results [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF][START_REF] Hoesch | Spin structure of the Shockley surface state on Au(111)[END_REF][START_REF] Ishizaka | Giant Rashba-type spin splitting in bulk BiTeI[END_REF] showing surface states, originating from the broken symmetry at the surface, which are spin-split by Rashba SOC. As previously discussed, we retrieve materials with high atomic number:

Z Au = 79, Z Ir = 77, Z Bi = 83, Z T e = 52.
Focusing on graphene, the Bychkov-Rashba Hamiltonian takes the form:

H BR = λ BR (τ σ x s y -σ y s x ) (2.33)
, and leads to the disperion relation: [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]). b) ARPES measurement of Au(111) (adapted from [START_REF] Hoesch | Spin structure of the Shockley surface state on Au(111)[END_REF]). c) ARPES measurement of spin-orbit split states of BiTeI (adapted from [START_REF] Ishizaka | Giant Rashba-type spin splitting in bulk BiTeI[END_REF]).

E ±,sz ( κ) = s z λ BR ± ( v F κ) 2 + λ 2 BR (2.34)
, where s z = 1 for spin-up bands and s z = -1 for spin-down bands. cone of graphene and induce a spin-splitting. However, the origin of SOC of some systems (hybridization or Rashba) is still discussed. In the following section, we present a short overview of such hybrid graphene/heavy metals systems.

Spin-Orbit Coupling induced in graphene

In the last decade, strong SOC have already been observed in graphene on different substrates, with a spin-splitting of the order of 1 -10 meV (already three orders of magnitude above the intrinsic SOC of graphene) and more recently, "giant" SOCinduces splitting of the order of 100 meV have been shown through intercalation of high atomic number material. Experimental observation of such SOC are mostly done by spin-dependent techniques such as spin-polarized STM (SP-STM) or spin-resolved ARPES (SARPES), or by measurements under magnetic field.

Considering the case of intrinsic SOC, a substrate with a high atomic number can induce SOC in graphene band structure by hybridization. It has been predicted and/or measured for different types of substrate such as semiconducting tungsten disulfide (W S 2 ) [START_REF] Taychatanapat | Spin-orbit proximity effect in graphene[END_REF][START_REF] Chen | Strong interface-induced spin-orbit interaction in graphene on WS2[END_REF], topological-insulating Sb 2 T e 3 [START_REF] Jin | Proximity-induced giant spin-orbit interaction in epitaxial graphene on a topological insulator[END_REF], transition metal dichalcogenides (TMDs) [START_REF] Lohmann | Strong electron-hole symmetric Rashba spinorbit coupling in graphene/monolayer transition metal dichalcogenide heterostructures[END_REF], ferromagnets (Ni [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], Co(0001)) [START_REF] Gong | Spintronic properties of graphene films grown on Ni(111) substrate[END_REF][START_REF] Rader | Is there a Rashba effect in graphene on 3d ferromagnets?[END_REF][START_REF] Dedkov | Rashba effect in the graphene/Ni(111) system[END_REF] and crystalline metals (Au [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], Ag [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], Pt [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], Ir( 111)) [START_REF] Wu | Spin-orbit splitting in graphene on metallic substrates[END_REF][START_REF] Klimovskikh | Nontrivial spin structure of graphene on Pt(111) at the Fermi level due to spin-dependent hybridization[END_REF][START_REF] Marchenko | Spin splitting of Dirac fermions in aligned and rotated graphene on Ir(111)[END_REF]. Table 2.1 shows the λ SO or the SO splitting for these substrates along with their atomic number. We observe that the induced SOC in graphene for most of these substrates is of the order of 1 -20 meV. It increases to 30, 50 and 80 meV for respectively Au [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Pt(111) (elements with the highest Z), confirming that the SOC strength is strongly dependent of the atomic number of the substrate.

On the other hand, extrinsic SOC can also be induced in graphene by the intercalation Exchange interaction induced in graphene by the spin-dependent hybridization with a ferromagnetic material (FM) leads to a new term in the effective Hamiltonian (equation 2.33) of the form:

Exchange interaction

H ef f = H 0 + H I + H BR + H ex (2.35
)

H ex = λ ex m. s (2.36)
, with the exchange parameter λ ex and magnetization orientation m. The effect of exchange interaction on graphene band structure are depicted in fig. 2.11. We can observe that the two interactions (SOC and exchange interaction) simultaneously induced in graphene can make the bands anisotropic with respect to the magnetization orientation.

A typical building block in spintronics is comprised of ferromagnet/nonmagnet structures, so one of the key question in graphene spintronics is to develop a systematic understanding of the Gr/FM interfaces. Proximity-induced exchange interaction in graphene has been observed or predicted for several ferromagnetic insulating substrates such as

EuO [START_REF] Swartz | Integration of the ferromagnetic insulator EuO onto graphene[END_REF][START_REF] Haugen | Spin transport in proximityinduced ferromagnetic graphene[END_REF][START_REF] Su | Effect of intervalley interaction on band topology of commensurate graphene/EuO heterostructures[END_REF], EuS [START_REF] Heiman | Strong interfacial exchange field in the graphene/EuS heterostructure[END_REF] and Y IG (Yttrium Iron Garnet, Y 3 F e 5 O 12 ) [START_REF] Shi | Proximity-Induced Ferromagnetism in Graphene Revealed by the Anomalous Hall Effect[END_REF][START_REF] Leutenantsmeyer | Proximity induced room temperature ferromagnetism in graphene probed with spin currents[END_REF] or antiferromagnetic insulators such as BiF eO 3 [START_REF] Zhang | Quantum Anomalous Hall Effect in Graphene Proximity Coupled to an Antiferromagnetic Insulator[END_REF][START_REF] Ren | Magnetic proximity effect in graphene coupled to a BiFeO3 nanoplate[END_REF]. These substrates being insulating, the exchange induced in graphene band structure could only be used for spin transport [START_REF] Shi | Proximity-Induced Ferromagnetism in Graphene Revealed by the Anomalous Hall Effect[END_REF][START_REF] Heiman | Strong interfacial exchange field in the graphene/EuS heterostructure[END_REF]. Ferromagnetic behavior has also been reported for hydrogenated graphene [START_REF] Giesbers | Interface-induced room-temperature ferromagnetism in hydrogenated epitaxial graphene[END_REF][START_REF] Fabian | Spin transport in hydrogenated graphene[END_REF][START_REF] Soriano | Magnetism-Dependent Transport Phenomena in Hydrogenated Graphene: From Spin-Splitting to Localization Effects[END_REF] and the local magnetism of either hydrogen adatoms or magnetic impurities into graphene have been extensively studied [START_REF] Dugaev | Exchange interaction of magnetic impurities in graphene[END_REF][START_REF] Mallet | Atomic-scale control of graphene magnetism by using hydrogen atoms[END_REF]. after the intercalation of one monolayer of gold (adapted from [START_REF] Varykhalov | Electronic and Magnetic Properties of Quasifreestanding Graphene on Ni[END_REF]). c) Overall band structure of graphene on Co(0001) measured along the ΓM and the ΓK directions (adapted from [START_REF] Trauzettel | Intact Dirac Cones at Broken Sublattice Symmetry: Photoemission Study of Graphene on Ni and Co[END_REF]). d) Band structure of Gr/Au(1ML)/Co(0001) measured along the ΓK direction (adapted from [START_REF] Rybkin | Magneto-Spin-Orbit Graphene: Interplay between Exchange and Spin-Orbit Couplings[END_REF]).

The π band of graphene is shifted in both systems to higher binding energy about 2.8

eV. Several contradictory experimental results have been published about this effect on either bulk FM (Ni [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Co(0001)) or ultrathin FM films. Some authors show an intact Dirac cone with preserved linear dispersion [START_REF] Trauzettel | Intact Dirac Cones at Broken Sublattice Symmetry: Photoemission Study of Graphene on Ni and Co[END_REF][START_REF] Marchenko | Highly spin-polarized Dirac fermions at the graphene/Co interface[END_REF] while others observed destroyed Dirac cones [START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF], or a cone-like dispersion near Fermi level but with a Fermi velocity divided by 10 [137]. The interpretation is still unclear, as the mechanisms behind this effect (SOC, exchange interaction, sublattice symmetry breaking). However, the strong hybridization between graphene and Ni (Co) has been shown to induce a magnetic moment in carbon atoms of the graphene layer of 0.05 -0.1 µ B per atom ( 0.1 µ B ) [START_REF] Weser | Induced magnetism of carbon atoms at the graphene/Ni(111) interface[END_REF][START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF]. This magnetic moment increases to 0.2 -0.25 µ B per atom when one monolayer of Fe is intercalated between Gr and Ni(111) [START_REF] Weser | Electronic structure and magnetic properties of the graphene/Fe/Ni(111) intercalation-like system[END_REF].

In order to conserve the Dirac cone at the K point of the BZ, intercalated systems

Graphene growth

This section is proposing a brief state of the art concerning graphene growth, focusing on high crystalline quality graphene grown on a metallic substrate. In the following, different graphene growth methods on metal substrates are discussed, followed in the next section by a non-exhaustive presentation of the intercalation process.

To obtain a high crystalline quality graphene, it has to be grown in an ultra-high vacuum environment (UHV) in order to prevent pollution from molecular gases or any molecules present in the air. UHV guarantees the cleanness of the grown sample and allows also epitaxial growth methods to achieve a high quality crystal. Two main techniques are employed in a UHV environment: carbon segregation or chemical vapor deposition (CVD). The first technique is used for metallic substrate with a high solubility for carbon atoms [START_REF] Yang | Solubility and diffusivity of carbon in metals[END_REF]. By annealing the substrate at high temperatures, carbon atoms segregate to the sample surface and then organize themselves into a graphene layer.

Either the small carbon impurities in nominally clean samples are used, or the samples are first doped with carbon [START_REF] Hamilton | Carbon segregation to single crystal surfaces of Pt[END_REF]. Macroscopic graphene layers have been achieved on different metallic substrates by this method [START_REF] Sutter | Graphene on Pt(111): Growth and substrate interaction[END_REF][START_REF] Liu | Universal segregation growth approach to wafer-size graphene from non-noble metals[END_REF]. CVD, also called decomposition method, is using hydrocarbon molecules, mostly ethylene, as a precursor for graphene growth. The hydrocarbon molecules are either adsorbed at room temperature (RT)

followed by an annealing procedure, or the molecules are directly adsorbed on the hot sample. The high temperature step is necessary in order to decompose the molecules and desorb the hydrogen atoms. In such a procedure, the metallic substrate acts as a catalyzer for the reaction. Graphene layers have been grown by CVD on many different metallic substrates such as Cu, Co, Ni, Ir, Ru, Pt, Rh [START_REF] Ago | Epitaxial chemical vapor deposition growth of single-layer graphene over cobalt film crystallized on sapphire[END_REF][START_REF] Loginova | Factors influencing graphene growth on metal surfaces[END_REF][START_REF] Sasaki | Moiré contrast in the local tunneling barrier height images of monolayer graphite on Pt(111)[END_REF][START_REF] Losurdo | Graphene CVD growth on copper and nickel: Role of hydrogen in kinetics and structure[END_REF][START_REF] Castner | LEED and thermal desorption studies of small molecules[END_REF]. For both methods, the graphene growth can easily be restricted to a single layer. For CVD method this saturation can be understood from the fact that this process involves a chemical reaction on the active metal surface, so it is strongly suppressed once the surface is fully covered. For the segregation method, one explanation is the thermodynamic stability of a single layer of graphene with respect to bulk graphite so that multilayers growth can be avoided by controlling the temperature. Most of these films are not aligned with the metal surface registry, excepted for some six-or threefold symmetric surfaces for which perfectly ordered epitaxial layers have been obtained.

In most cases, these ordered layers display moiré pattern with large periodicities due This large periodicity is also visible by low-energy electrons diffraction (LEED). In the particular case of Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], fig. 2.15 shows different LEED patterns both from the litterature and from our own measurements. The pattern consist in two main spots (inner spot due to Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and outer spot due to graphene) which are surrounded by smaller satellite spots reflecting the periodicity of the moiré.

The low Gr/Ir interaction, together with the self-limiting growth of graphene on Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] by CVD are the main reasons for our choice of Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] as a substrate for our hybrid systems. Growth of graphene by CVD on Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] has been extensively studied under many aspects. The main parameter to be controlled to obtain a high quality monolayer of graphene on Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] by CVD is the temperature [START_REF] Michely | Growth temperature dependent graphene alignment on Ir(111)[END_REF]. At low temperature (< 1400 K), graphene forms typically rotational domains [START_REF] N'diaye | Structure of epitaxial graphene on Ir(111)[END_REF][START_REF] Loginova | Defects of graphene on Ir(111): Rotational domains and ridges[END_REF] and the graphene layer itself presents several defects such as pentagon-heptagon rings, dislocations and grain boundaries [START_REF] Coraux | Structural coherency of graphene on Ir(111)[END_REF]. The density of such defects increases with decreasing annealing temperature.

Increasing the annealing temperature (above 1500 K) allows to obtain a graphene layer

d) e) f) a) b) c) Figure 2
.14: a) is a 5x4 nm 2 topographic image with atomic resolution of Gr/Ru(0001) taken at -0.05V, 1nA (adapted from [START_REF] Marchini | Scanning tunneling microscopy of graphene on Ru[END_REF]). b) is a topographic image of Gr/Cu(111) (adapted from [START_REF] Gao | Epitaxial graphene on Cu(111)[END_REF]). c) is an image of Gr/Ir(111) taken at 0.3V, 0.3nA (adapted from [START_REF] Sun | Topographic and electronic contrast of the graphene moiré on Ir(111) probed by scanning tunneling microscopy and noncontact atomic force microscopy[END_REF]). d) and e) are two images of two different rotational domains of Gr/Au(111) (adapted from [START_REF] Nie | Scanning tunneling microscopy study of graphene on Au(111): Growth mechanisms and substrate interactions[END_REF]). d) is a 6x6 nm 2 taken at (-0.1V, 0.3nA) for 11 • rotational domain. e) is a 5.9x5.9 nm 2 taken at (0.1V, 0.3nA) for 1.5 • rotational domain. f) is a schematic representation of a moiré pattern (adapted from [START_REF] N'diaye | Structure of epitaxial graphene on Ir(111)[END_REF]).

perfectly aligned with the atomic arrangement of the substrate and with an extremely low density of defects [START_REF] Michely | Growth temperature dependent graphene alignment on Ir(111)[END_REF][START_REF] N'diaye | Selecting a single orientation for millimeter sized graphene sheets[END_REF]. Partially graphene covered Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] surface by rotationally aligned graphene flakes has also been achieved using a different growth method [START_REF] Poelsema | Growth of graphene on Ir(111)[END_REF].

This is called Temperature-Programmed Growth (TPG). Instead of exposing the hot Ir surface (in the temperature range between 900 and 1500 K) to ethylene, one first saturate the Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] surface with ethylene molecules at room temperature (RT) and then flash the sample at a chosen temperature (in the same range). This method allows multiple nucleation centers for graphene growth to form on the substrate and the short time of flashing prevents a full monolayer to grow. The result are several different graphene flakes with the same orientation, whose size and density depend on the flashing temperature and on the quality of the Ir(111) surface [START_REF] Poelsema | Growth of graphene on Ir(111)[END_REF]. By repeating the TPG step, we can increase the number of flakes and keep a high number of edges. This method allows to tune the graphene surface coverage and still keep a high crystalline quality and a single crystal orientation.

In this work, our main goal is to study graphene on single atomic layers. As shown in previous paragraphs, a high crystalline quality graphene requires high temperature ( 1400 K), either by CVD or by TPG. At these temperatures, any metallic atomic films previously grown on the substrate will start forming an alloy with Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], dissolve into the Ir bulk, dewet from the surface or more simply desorb. So to study graphene interfaces with different materials, we must grow the metallic thin films after the graphene layer. The best way to grow such films between graphene and its substrate is by intercalation.

Co intercalation under graphene

Since discovery of graphene, the scientific community has studied the electronic and structural properties of graphene interfaced with a large variety of other materials. One efficient way to interface graphene with an other material is the intercalation between graphene and its substrate. Several hundreds of examples of intercalation of different elements below graphene can be found in literature. The intercalation mechanism has been proven to be element, substrate and temperature dependent [START_REF] Lacovig | Key role of rotated domains in oxygen intercalation at graphene on Ni(111)[END_REF][START_REF] Voloshina | Restoring a nearly free-standing character of graphene on Ru(0001) by oxygen intercalation[END_REF][START_REF] Halle | Filling the Gap: Li-Intercalated Graphene on Ir(111)[END_REF][START_REF] Sandin | Multiple coexisting intercalation structures of sodium in epitaxial graphene-SiC interfaces[END_REF][START_REF] Hofmann | Sequential oxygen and alkali intercalation of epitaxial graphene on Ir(111): enhanced many-body effects and formation of pn -interfaces[END_REF][START_REF] Pacilé | Artificially lattice-mismatched graphene/metal interface: Graphene/Ni/Ir(111)[END_REF][START_REF] Vlaic | Cobalt intercalation at the graphene/iridium (111) interface: Influence of rotational domains, wrinkles, and atomic steps[END_REF]. Therefore, making an exhaustive review of the intercalation process is far beyond the scope of this thesis. We would like, in this section, to discuss briefly the intercalation mechanisms of Co between graphene and Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and to address some structural properties of the hybrid which will be quite helpful for the following chapters.

On the contrary Pd intercalation has not yet been extensively studied by the scientific community and it will be addressed in the following chapters.

When deposited at RT, Co forms randomly distributed clusters at the surface of Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF].

By further annealing, Co intercalates by two different mechanisms depending on rotational domains and annealing temperature: through step edges and through defects such as wrinkles (intercalation "from the top") [START_REF] Vlaic | Cobalt intercalation at the graphene/iridium (111) interface: Influence of rotational domains, wrinkles, and atomic steps[END_REF] or through the graphene flake edges (intercalation "from the side") [START_REF] Vlaic | Intercalating cobalt between graphene and iridium ( 111 ): Spatially dependent kinetics from the edges[END_REF]. The role of wrinkles and substrate step edges in the intercalation process can be explained by a nucleation center for Co clusters, causing defects in the underneath graphene and finally allowing Co atoms to go below the graphene layer. Intercalation through defects of a full graphene monolayer has also been reported

for Fe [START_REF] Bazarnik | Multi-layer and multicomponent intercalation at the graphene/Ir(111) interface[END_REF]. However, intercalated Fe forms preferentially small areas in the middle of terraces, while Co forms larger areas located at the Ir(111) step edges. One explanation is that intercalated cobalt atoms diffuse very slowly under the graphene layer (typical diffusion length of few hundreds of nanometers) and are easily pinned by atomic iridium steps. To improve cobalt intercalation, one can increase the annealing temperature in order to make cobalt atoms move faster under graphene. However, one has to be careful about the surface alloying between cobalt atomic layer and the underneath metallic substrate, which can induce strong effects on the sample band structure. Surface alloying between Co and Ir has indeed been shown to happen around a temperature of 770K [START_REF] Drnec | Surface alloying upon Co intercalation between graphene and Ir(111)[END_REF].

Once Co, or even others ferromagnetic materials, are intercalated between Gr and Ir, the graphene layer shows a strong moiré corrugation with respect to the one of Gr/Ir, indicating a stronger Gr-intercalant interaction. Some STM topographic images are depicted in fig. 2. [START_REF] Lee | Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene[END_REF]. We clearly see an increase of the moiré contrast between intercalated and non-intercalated regions. In the case of intercalated Co, the lateral periodicity and orientation of the moiré is identical to the one of Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], which suggests that the Co layer underneath graphene is pseudomorphic with the Ir(111) lattice [START_REF] Decker | Atomic-scale magnetism of cobalt-intercalated graphene[END_REF].

For our work, any rotational domains in graphene must be avoided in order to have a well increase the defect density for the intercalation "from the top" or increase the number of flake edges for the intercalation "from the side". Both strategies have heavy consequences on the ARPES measurement of the band structure of the sample. Too many defects lead to a less defined band structure and a high density of graphene flake edges (grown by TPG as explained in section 2.3) diminishes the signal because of the uncovered parts of the sample. We tried both strategies and finally find a compromise: TPG growth of high quality graphene for a choosen flake density and cobalt deposition at high temperature (still under the intermixing limitation). The results and the structural study of these samples will be further discussed in chapter 4.

Chapter 3

Experimental methods

This chapter presents a short description of the main experimental techniques used in this thesis work. These are Scanning Tunneling Microscopy (STM) and Angle-Resolved Photo-Emission Spectroscopy (ARPES). The first one provides information about the nanostructure morphology with atomic resolution. ARPES provides information on the occupied band structure of the surface of the sample. After a brief introduction to these two techniques, the experimental set-up used for this thesis work is presented with a short description of the daily experimental procedure.

Scanning Tunneling Microscopy

Gerd Binning and Heinrich Roher have invented the Scanning Tunneling Microscopy in 1981 [START_REF] Binnig | Surface studies by scanning tunneling microscopy[END_REF][START_REF] Binnig | Scanning tunneling microscopy[END_REF]. This technique owes its great popularity to the ability of giving atomic scale imaging coupled with the capability to extract information on the electronic structure of surfaces on a local scale. In the following, it is provided a basic introduction to the physics underlying tunneling microscopy. The STM is based on the concept of quantum tunneling. When a sharp conducting tip is brought very close to the conducting surface to be examined (≈ 5 -10 Å), a bias voltage applied between the two allows electrons to tunnel through the vacuum between them. The resulting tunneling current depends on the overlap of the tip and sample electron wave functions. This implies that the tunneling current is a function of tip position, applied voltage, and tip and sample local density of states (LDOS) [START_REF] Chen | Introduction to scanning tunneling microscopy[END_REF]. Bardeen and furthermore developed by Tersoff and Hamman [START_REF] Tersoff | Theory and application for the scanning tunneling microscope[END_REF] and Baratoff [START_REF] Baratoff | Theory of scanning tunneling microscopy -methods and approximations[END_REF].

In Bardeen treatment the system is simplified to two parallel plates with negligible interactions separated by an insulator [START_REF] Bardeen | Tunneling from a many-particle point of view[END_REF]. The tunneling current is then evaluated from the overlap of the wave functions of the tip, ψ ν , and the sample, ψ µ , in the separating region [START_REF] Wolf | Principles of electron tunneling spectroscopy[END_REF]: , where the summation goes over all quantum states µ and ν of the unperturbed sample and tip. T µ,ν is the tunneling matrix element, E µ and E ν are the eigenvalues given with respect to the (common) Fermi level, V is the applied voltage between the electrodes, f(E, T) is the Fermi-Dirac distribution function and T is the temperature. The δ-function indicates energy conservation implying that the electron tunnels from one electrode to the other is an elastic process, whereas the Fermi-Dirac functions take into account that tunneling occurs from filled to unfilled states. In the limits of small voltage and temperature, equation 3.1 becomes:

I(V ) = 4πe µ,ν |T µ,ν | 2 δ(E µ -eV -E ν ) × (f (E µ -eV, T )[1 -f (E ν , T )]- f (E ν , T )[1 -f (E µ -eV, T )]) (3.1)
I(V ) = 2π e 2 V µ,ν |T µ,ν | 2 δ(E µ -E F )δ(E ν -E F ) (3.2)
The tunnel matrix element T µ,ν represents the overlap in the gap region of the electrode wave functions and is given by the current density operator through a surface S 0 lying entirely within the gap region:

T µ,ν = -2m e S 0 dS(ψ * ν ψ µ -ψ µ ψ * ν ) (3.3)
The main difficulty in this approach consists in evaluating T µ,ν . In 1961 Bardeen presented his results considering two planar electrodes. A more realist picture of the wave functions has been given by Tersoff and Hamann. The surface wave function ψ ν is described by a set of periodic surface plane wave functions decreasing exponentially in the normal direction (z). The tip wave functions are the solutions of the Schrödinger equation for a spherical potential wall (s-wave approximation). Within these approximations and for low bias voltages compared to the electrode work function and low temperature, the tunneling current becomes [START_REF] Lang | Spectroscopy of single atoms in the scanning tunneling microscope[END_REF]:

I(V ) ≈ eV 0 dEρ t (E -eV )ρ s (r t , E) (3.4)
where ρ t (E) is the density of states associated with the tip atom; ρ s (r t , E) is the LDOS of the sample and r t is the position of the tip center with respect to the surface. ρ s (r t , E) can be expressed as:

ρ s (r t , E) ≈ ρ s (E)exp(-2z 2m φ ) (3.5)
where φ is the average value of the tunneling barrier with respect to the Fermi energy and ρ s (E) is the density of states associated with the sample atom right under the tip.

The average energy barrier reads as:

φ = φ t + φ s 2 + eV 2 -E (3.6)
These approximations lead to two important results: a) the tunnel current behaves exponentially with distance z between the tip and the sample, b) assuming a constant LDOS for the tip, in constant current mode STM measurements can be interpreted as a map of constant ρ s (E F ) of the surface. The first result implies that the tip apex atom dominates the tunneling process (for φ = 4 eV, a 1 Å displacement in z implies a ten-fold variation in I), explaining the STM atomic-scale probing capabilities. The second result comes from the fact that the largest contribution to the integral in equation 3.4 comes from the highest energy states of the sample. The atomic corrugation imaged by an STM is therefore the modulation of the LDOS surface of the sample. As a consequence, with STM measurements one cannot strictly speak about "height" and in the following we will refer to apparent height when a description of STM topography will occur.

Angle-Resolved PhotoEmission Spectroscopy

The photoelectrons spectroscopy, or photoemission, is a technique based on the photoelectric effect discovered by Hertz in 1887 [START_REF] Hertz | On the photoelectric effect[END_REF] and explained by Einstein in 1905 [START_REF] Einstein | A heuristic point of view about the generation and transformation of light[END_REF],

giving access to the occupied electronic states of a solid. In fact, when a solid is shined with a photons beam (typically UV or X-ray light) with energy hν higher than its work function, it can emit electrons with a kinetic energy E kin following the conservation law:

hν = E kin + E B + φ (3.7)
, where E B (> 0) is the binding energy of the initial state of the electron in the solid, defined by the Fermi level and φ the work function of the material. The different energies at play in the photoemission process are represented in fig. 3.2.

We usually distinguish two kinds of photoemission spectroscopy, according to their incident beam energy: UV photoemission (UPS) which allows to probe the valence bands (hν < 100 eV) and the X-rays photoemission (XPS) which allows to probe core levels (hν = 0.1-10 keV). The core levels energies are mostly depending on the chemical nature of the different elements of a material and their bonds. XPS is therefore a powerful tool of chemical analysis for thin layers. UPS, instead, can probe the band structure of a crystal, within some approximations detailed below. In the case of angle-resolved photoemission, the photoemitted electrons (or photoelectrons) are usually collected by a hemispherical analyzer (depicted in fig. 3.2) which discriminates them depending on their kinetic energy and their angle, achieving, on a bidimensionnal detector, an intensity map function of E kin and θ. Being the experimental technique at the core of this thesis work, we will now discuss in some details angle resolved photoemission spectroscopy and its use to probe valence bands of crystalline materials.

ARPES: a three-step model

Many approaches have been proposed over the years to interpret the photoemission spectra [START_REF] Berglund | Photoemission studies of copper and silver: theory[END_REF][START_REF] Mahan | Angular dependence of photoemission in metals[END_REF][START_REF] Mahan | Theory of photoemission in simple metals[END_REF][START_REF] Kevan | Angle-resolved photoemission: theory and current applications[END_REF][START_REF] Hüfner | Photoelectron spectroscopy: principles and applications[END_REF]. The one-step model proposed by Mahan in 1970 treats the light-matter interaction Hamiltonian pertubatively to express, thanks to the Fermi golden rule, the transition probability between the initial and the final states of the photoelectron [START_REF] Mahan | Theory of photoemission in simple metals[END_REF]. However the description of the final state, particularly around an interface, is very difficult and requires many approximations. The three-steps model, first introduced by Berglund and Spicer [START_REF] Berglund | Photoemission studies of copper and silver: theory[END_REF], decomposes the phenomenon in three independent processes: an optical excitation of the electrons between two Bloch states of the solid, the transfer of these photoelectrons to the surface, and finally the crossing of this surface into vacuum. This model is widely used because it establishes the transformation rules giving access to the initial wavevector from the kinetic energy and the angle of the photoelectron.

Optical excitation

During the photoemission process, an electron absorbs a photon with energy hν and goes from an initial Bloch state |φ k i to an unoccupied final state |φ k f . For this transition in the UV regime, the momentum of the photon can be neglected leading to the conservation laws:

k f = k i (3.8) E f = E i + hν (3.9)
The photoelectron can then leave the system only if its energy is higher than the one of vacuum. In the case of a periodic crystal, the wavevector conservation law is also valid modulo a reciprocal space lattice vector, giving:

k f = k i + G.
The photoemission intensity is directly proportional to the transition probability between these two states, described by this matrix element of the interaction Hamiltonian:

M f i = φ k f |H int |φ k i (3.10)
To describe the absorption of a photon by an electron, we can first consider an Hamiltonian of the form:

H = H 0 + H int (3.11)
, with H 0 the Hamiltonian of the electron without incident photon:

H 0 = p 2 2m + V (3.12)
, where V is the potential energy due to all other particles of the system. We will now derive the photon-electron interaction Hamiltonian as the Hamiltonian of a charged particle in an electromagnetic field. For a field that varies in time and in space, the electrodynamic potential must be expressed in terms of both A( r, t) (the vector potential)

and ϕ( r, t) (the scalar potential). Choosing the Coulomb gauge such that ϕ = 0, leads to a plane-wave description of E and B:

E = - ∂ A ∂t (3.13) ∇. A = 0 (3.14) B = ∇ × A (3.15)
Now, starting with the Lorentz force on a particle with charge q, F = q( E + v × B), we can express the total potential energy U and the Lagrangian L as:

U = qϕ -q v. A (3.16) L = m v 2 2 + q v. A -qϕ (3.17) Recognizing p = ∂L ∂ v = m v + q A, we write v = 1 m ( p -q A)
and then obtain:

H int = p. v -L = [ p -q A( r, t)] 2 2m + qϕ( r, t) (3.18)
Remembering the Coulomb gauge (ϕ = 0) and ∇. A = 0, we can then derive:

∇. A = ( ∇. A) + A. ∇ = 0 (3.19)
, and with p = -i ∇:

[ p, A] = 0 (3.20)
We finally obtain for the interaction Hamiltonian:

H int = 1 2m (-2q A. p + q 2 | A| 2 ) (3.21)
Generally the last term is considered small compared to the cross term. This term should be considered for extremely high field strength, which is nonperturbative and significantly distorts the potential binding atoms together. One can estimate that this would start to play a role at intensity levels > 10 15 W/cm 2 , which may be observed for very high energy and tightly focused pulsed femtosecond lasers. In our case, we can neglect the term in | A| 2 . Moreover, if the wavelenght of the field is much larger than the crystalline lattice dimensions (which is the case in the UV regime), we have k → 0 and so e i k. r ≈ 1. This is known as the dipolar approximation consisting in neglecting the spatial variation of the potential vector:

A( r, t) = A 0 (ω) (3.22)
The matrix element becomes then:

|M f i | 2 = q 2 2 m 2 | φ f | ∇|φ i . A 0 | 2 (3.23)
And the Fermi golden rule gives us the transition probability per unit of time:

ω f i = 2π |M f i | 2 δ(E f -E i -hν) (3.24)

Transfer to the surface

During this process, the photoelectrons propagate toward the surface to be finally emitted in vacuum. However in its way to the surface, an electron can encounter inelastic collisions, loosing information on its initial wavevector and energy, contributing therefore to the inelastic scattering background. Most of the collected electrons which are not scattered on their way to the surface come from a depth in the solid lower than their mean free path. This mean free path is highly dependent on the energy of the incident photons. The phenomenological "universal curve" of mean free path with respect to excitation energy is given in fig. 3.3 and it reveals a minimum in the UV regime. For a typical excitation of 21.2 eV, the distance travelled by electrons without collisions is of the order of 10 Å, meaning few atomic planes. The UPS is so particularly adapted to the study of thin layers and interfaces, or of bidimensionnal surface states of a bulk crystal.

Crossing the surface

In the directions parallel to the surface, the parallel component of the wavevector -→ k is conserved, so that the momentum of the photoelectron outside the solid can be written:

--→ p ext = --→ k ext = ( - → k + -→ G ) (3.
k ext = k = 2m 2 E kin sin θ (3.26)
, with θ the emission angle with respect to the normal direction and E kin its kinetic energy. Numerically, the commonly used formula becomes:

k = 0.512Å -1 E kin (eV ) sin θ (3.27)
The maximum value for the kinetic energy is the one of the electrons initially at the Fermi level:

E max kin = hν -φ (3.28)
,where φ is the work function of the sample. In consequence, the maximal parallel wavevector we can reach is energy dependent and is expressed by:

k max = 2m 2 (hν -φ) (3.29)
Moreover, an uncertainty on the angle ∆θ leads to an uncertainty in momentum:

∆k = 0.512Å -1 E kin (eV ) cos θ∆θ (3.30)
For a same angular resolution ∆θ, the resolution in momentum increases (∆k decrases) by diminishing the photons energy.

In the perpendicular direction, the photoelectron can leave the solid only if its kinetic energy is higher than a surface potential. If we consider the final state being described by the free electrons model, we must have:

2 2m k 2 ⊥ ≥ V 0 (3.31)
, with V 0 = E v -E 0 the vacuum energy measured with respect to the band minimum E 0 and k ⊥ the perpendicular component of the wavevector. Its relation to the kinetic energy is then:

k ⊥ = 2m 2 E kin cos 2 θ + V 0 (3.32)
In this direction, the wavevector is so not conserved and the V 0 potential is acting as a momentum reservoir. This potential can be either estimated by a band structure calculation or experimentally determined.

Summary of the three steps

From these three steps, we can obtain the intensity of the signal for a given kinetic energy and momentum:

I(E kin , hν, p, θ) ≈ f,i |M f i | 2 f (E i )δ(E f -E i -hν)δ(E kin -E f -φ) δ( k -k i -G)δ( - → k - - → p - -→ G ) (3.33)
, with f(E) the Fermi function. All the δ-functions express the different conservation laws.

If the matrix element is a constant, the intensity is proportional to the density of the occupied states. This hypothesis allows a first rough interpretation of the photoemission spectra. However the modulation of the matrix element with respect to the angle, the polarization or the energy can induce strong modifications of the measured intensity, called "matrix element effects". We saw for example that the matrix element is directly proportional to A 0 , therefore the intensity of the signal will not be the same for a spolarization (in plane) or a p-polarization (perpendicular to the plane). To address the matrix element effect in photoemission is beyond the scope of this thesis work (for an exhaustive overview, see [START_REF] Moser | An experimentalist's guide to the matrix element in angle resolved photoemission[END_REF]).

Experimental set-up

In this section, the different parts of the ARPES experimental set-up are presented. Fig. 3.4 shows a photograph of the ARPES experimental set-up with its four main parts highlighted in different colours, namely the preparation chamber (green), the ARPES chamber (red), the light source (yellow) and the analyzer (blue). The most important parts of the set-up will now be further detailed.

Ultra-high vacuum

Photoemission spectroscopy requires ultra-high vacuum (UHV) environment for two main reasons. First of all, UV light requires a high enough vacuum because the gases, including air, absorb the UV. Moreover, for pressure above 10 -5 -10 -6 mbars, the photoelectrons are also absorbed. On the other hand, the main reason for keeping an UHV environment is the great sensibility of this technique to the surface sample.

We already saw that ARPES is probing the sample on a depth of the order of few

Light source

We used as a photon source a helium discharge lamp. Helium is the most commonly used gas for this type of lamp because it has a low number of transitions and also because it

Goniometer

The sample is placed in a homemade 6-axes goniometer (3 linear axis x, y, z and three rotations θ, φ and ψ).

Data representation

After the experiment, we obtain an intensity matrix I(E, θ, ϕ) with θ our measurement angle and ϕ the angle in the hemispherical analyzer (see appendix A). We can easily transform the data in the reciprocal space to obtain I(E, k x , k y ) with: As it has been presented in the previous chapter, the atomic arrangements of graphene and its substrate (Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] These are:

k x (Å -1 ) = 0.512 E kin (eV ) sin θ cos ϕ (3.34) k y (Å -1 ) = 0.512 E kin (eV ) sin ϕ (3.35)
-pΓK Gr which shows the electronic dispersion in the (k y , E) plane at k x = 1.703 Å -1

(perpendicular to the ΓK direction at K Gr ).

-pΓK Ir which shows the electronic dispersion in the (k y , E) plane at k x = 1.543 Å -1

(perpendicular to the ΓK direction at K Ir ).

-M Gr K Gr Γ direction.

-M Ir K Ir Γ direction.

ARPES data can also be represented by constant energy maps, showing the electronic dispersion in the (k x , k y ) plane at a chosen energy. Examples of these representations are given in fig. 3.7 for a sample of Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. We show pΓK Gr , pΓK Ir , M Gr K Gr Γ, M Ir K Ir Γ and a constant energy map taken at -0. Chapter 4

Structural properties of graphene based hybrid systems

In this chapter we focus our attention on the growth mechanisms and the structural properties of the graphene based hybrid systems described in chapter 1. This investigation has been performed in collaboration with Pr. Mikhail Fonin at Konstanz University where I was visiting scientist for one month. As it will be explained in detail in the following, the sample preparation consisted in several steps. First a graphene layer was grown on a Ir(111) substrate, then a single atomic layer of a chosen material (Co or Pd) was intercalated between graphene and Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. The structural properties of the different growth steps are analyzed mostly by means of STM.

Co intercalation under a complete graphene layer

As already discussed in section 2.4, the intercalation process is element dependent and the path for intercalation changes depending on the growth procedure. Several parameters need therefore to be optimized to achieve the desired system. Previous studies have shown ARPES measurements of Co intercalated between graphene and Ir(111) samples ( [START_REF] Pacilé | Electronic structure of graphene/Co interfaces[END_REF][START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF]). In such cases, the sample preparation has been done by room or low temperature deposition of Co, followed by an annealing to an "unprecised temperature" higher than 500 • C. The resulting band structure is normally of poor quality close to the Fermi level. We therefore decided to attempt a novel approach by depositing Co at 400 The periodicity of both moiré patterns is 2.6±0.15 nm, indicating the pseudomorphic growth of Co on Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. evaporated Co is forming large 3D clusters on top either of bare Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] or Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF].

We estimated the surface of intercalated Co to be 3%.

In order to increase the amount of intercalated Co we rose the annealing temperature to 500 • C while keeping the same amount of deposited Co (see fig. of a surface alloy between Ir and Co taking place at a temperature between 400 • C and 500 • C [START_REF] Drnec | Surface alloying upon Co intercalation between graphene and Ir(111)[END_REF].

These topographic experiments show that the quantity of Co which intercalates under graphene is very low for the chosen intercalation conditions. A possible alternative strategy consists in taking advantage of the graphene flake edges and performing an intercalation "from the side". Such an intercalation requires a graphene with a high density of large percolating flakes which can be grown by TPG, as discussed in section 2.3. It has been shown that, with such growth conditions, the intercalated Co can diffuse below graphene forming patches of several hundreds of nanometers [START_REF] Vlaic | Intercalating cobalt between graphene and iridium ( 111 ): Spatially dependent kinetics from the edges[END_REF][START_REF] Vlaic | Graphene as a Mechanically Active, Deformable Two-Dimensional Surfactant[END_REF].

Temperature-programmed growth of graphene

In order to obtain a graphene layer with a high density of flake edges, graphene has In this part we concentrate on graphene growth, therefore we will not address the change in the moiré corrugation visible under certain Gr flakes, which will be discussed in the following sections. A first look confirms immediately that the graphene surface coverage is increasing with respect to the number of TPG cycles. The graphene surface coverages are estimated to be 53% (TPG1) and 74% (TPG2) on Crystal 1, and 32% (TPG1), 50%

(TPG2) and 65% (TPG3) on Crystal 2. These surface coverages have been measured

by averaging over multiple images of different regions of the sample, the total examined surface being for each sample superior to 1 µm 2 . Since the growth parameters are identical for both crystals, the difference of surface coverages can only be explained by the crystal itself. This difference can originate from a difference in iridium purity, leading to different carbon segregation, or macroscopic defects influencing the crystal surface. Besides, Ir atomic steps appear to play a key role in the growth of graphene.

Most of graphene flakes are indeed pinned to an atomic step of the substrate, while very few small flakes are located on the middle of a substrate terrace, suggesting that these steps favor the graphene nucleation and growth. proving the absence of rotational domains for the three TPG samples. In the following, for sake of simplicity, the total coverage of graphene will be indicated by the percentage of Ir surface covered. For example 50% graphene corresponds to a TPG growth of graphene on Ir(111) until a surface coverage of 0.5 ML.

Intercalation "from the side": Co and Pd

As shown in the previous section the growth of graphene by TPG allows to form an incomplete graphene layer with large flakes and a high density of edges. In order to study the intercalation "from the side" we deposited the intercalant (Co or Pd) at 400 • C on a 50% graphene covered Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] surface. This deposition was followed by a 30 min annealing at the same temperature. To identify both intercalated materials, we focused on the moiré patterns of intercalated domains (fig. 4.9). The apparent height profiles As expected, both intercalated materials are immediately identified thanks to their strong moiré pattern with respect to graphene. The majority of intercalated domains for both Pd and Co grow at the lower part of an atomic terrace of the substrate. All the deposited Co appears intercalated under graphene, while Pd is both intercalated under graphene and laying on bare Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. The non-intercalated Pd forms 2D islands pinned to the substrate atomic steps (yellow domains in fig. 4.11). We measured 14% With these measurements, it appears that Co intercalation under graphene is energetically favorable. There is indeed an energy barrier for intercalation [START_REF] Vlaic | Intercalating cobalt between graphene and iridium ( 111 ): Spatially dependent kinetics from the edges[END_REF] but the intercalated state is at much lower energy i.e. Co atoms can not escape once intercalated. The situation for Pd seems different. Although we do not have enough data to perform a proper analysis of the following assumption, it appears that the asymmetry of the energy landscape is much less pronounced than for Co, therefore, the quantity of intercalated Pd with respect to Pd/Ir is varying from region to region on the same sample. In order to test the efficiency of this sample preparation we increased the amount of deposited material on the graphene-covered Ir(111) surface. Fig. 4.12 displays 500x500 nm 2 topographic images of 0.5 ML Co deposited with the same conditions on a 50% Gr.

It immediately appears that most of the graphene layer is laying on Co (red domains), while very few stays unintercalated (blue domains in fig. 4.12a) and b) right). We measured 49% of intercalated Co i.e. the totality of the deposited Co.

In the case of Pd, to promote the amount of intercalated graphene, we reduced the free Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] surface by rising the graphene surface coverage to 65%. We then measured the The difference is even more evident between the region 1 and 2 of the 0.5 ML deposition.

While most of the graphene is intercalated in region 1 with only small islands of Pd/Ir, region 2 reveals large islands of Pd/Ir and a small area of intercalated Pd. It appears that the intercalated amount of Pd depends strongly on the local morphology of the sample.

Despite the inhomogeneity of the sample, the total intercalated graphene coverage is 20% for 0.2 ML deposited and 35% for 0.5 ML deposited. Therefore, the rise of the deposited quantity of Pd results in the increase of the intercalated area, even though the area covered by Pd islands is also increasing.

In order to check for the possibility of a complete intercalation, we rose the deposited amount to 0.9 ML, well above the 65% of graphene coverage. The choice to remain in the submonolayer regime has been done to be able to identify Pd islands with respect to Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. This sample results in the complete intercalation of the 65% graphene layer, as shown in fig. 4.15. Large islands of Pd are also present on Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. However, for all measured samples, we never observe a double layer island of Pd on Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], confirming that the growth of 2D islands on Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and the intercalation under graphene are favored with respect to a 3D growth. For photoemission experiments shown in the next chapters we always deposited 1 ML of Pd thus ensuring a complete intercalation of graphene.

ARPES measurements of graphene

The use of TPG for graphene implies a not fully covered surface and, as seen in the previous section 4.2, an inhomogeneous coverage on different regions of the Ir(111) substrate. It is a priori not obvious that such a graphene has the same band structure that a complete graphene monolayer. Moreover, ARPES is a spectroscopic technique which averages the signal taken from the surface of the incident photon beam, which in our case has a size of one millimeter. A verification that the TPG-grown graphene have the same band structure as a complete graphene layer is therefore necessary. A detailed study of the electronic properties of Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] with respect to the number of TPG cycles has already been published [START_REF] Kralj | Graphene on Ir (111) characterized by angle-resolved photoemission[END_REF] and will be used as reference. Even though the electronic structure appears the same for the three graphene layers, a quantitative analysis is necessary to determine the quality of the ARPES measurements. -0,20 -0,15 -0,10 -0,05 0,00 0,05 0,10

M Gr ← K Gr → Γ 0.05 Å -1
Intensity (a.u.) measurement of a band width is the full width at half maximum (FWHM) [START_REF] Kralj | Graphene on Ir (111) characterized by angle-resolved photoemission[END_REF] but in our case, it can not be determined for all samples. Therefore, we report the half width at half maximum (HWHM). For the branch of the cone along the M Gr K Gr direction, we measured HWHMs of 0.041 Å -1 for TPG2, 0.031 Å -1 for TPG3 and 0.033 Å -1 for the complete graphene layer. Only the TPG2 sample shows an enhancement of its band width with respect to the complete graphene. However, along the K Gr Γ direction, a continuous decrease of the cone band width has been measured with 0.038 Å -1 , 0.032 Å -1 and 0.027 Å -1 for TPG2, TPG3 and the complete Gr respectively. Besides, the band peak is clearly emerging from the background noise level when going from TPG2 to the complete Gr. The same effect is displayed in reference [START_REF] Kralj | Graphene on Ir (111) characterized by angle-resolved photoemission[END_REF] where the cone branch appears progressively with respect to the TPG cycles number and becomes clearly visible at about a surface coverage between 0.5 and 0.6 ML.

Another method to quantify the differences in the dispersion of the Dirac cone between the different samples is to use the first-nearest neighbor tight-binding model (detailed in section 2.1.2) to fit the data. The fitting parameters values for the three graphene layers are displayed in table 4.1 along with the typical values for a quasi-freestanding graphene [START_REF] Reich | Tight-binding description of graphene[END_REF] and the fits are represented in ARPES images by red dashed lines in fig.

4.16a)-c

). The γ 0 and s 0 parameters are identical for all samples with respective values of -2.7 eV and 0.0, corresponding to a quasi-freestanding graphene. However, the ε 2p parameter, which corresponds to the doping of the cone at the K Gr point, is close to zero for a complete Gr (4.9 meV) while it increases to 40 meV for both TPG2 and TPG3 samples. This doping is consistent with literature [START_REF] Kralj | Graphene on Ir (111) characterized by angle-resolved photoemission[END_REF] in which a value of about 100 meV is found for a TPG-grown graphene. This doping effect is probably caused by the graphene flake edges which have a different interaction with the Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] substrate with respect to the rest of the flake [START_REF] Lacovig | Growth of dome-shaped carbon nanoislands on ir (111): the intermediate between carbidic clusters and quasi-free-standing graphene[END_REF].

With such analysis, we observed a sharpening of the π band of graphene with respect to the surface coverage and a small doping effect due to graphene flake edges. A further comparison of the different growth methods is presented in fig. 4.17 which

System

shows ARPES images of TPG3 (85% graphene) and a complete Gr layer taken along the -0,6 -0,4 -0,2 0,0 0,2

M Gr K Gr Γ direction
M Gr ← K Gr → Γ 0.2 Å -1 38 mÅ -1 54 mÅ -1 50 mÅ -1
Ir state e) EDC -M Gr K Gr at 0.7 Å -1 As a final analysis, we realized a linear fit of our data in the energy range from -0.8 eV to -0.4 eV to determine the Dirac cone slopes along both directions. We find the same values for both samples of 4.95 eV.Å -1 (0.75 × 10 6 m.s -1 ) for the M Gr K Gr direction and 6.20 eV.Å -1 (0.94 × 10 6 m.s -1 ) K Gr Γ direction, comparable to literature [START_REF] Kralj | Graphene on Ir (111) characterized by angle-resolved photoemission[END_REF].

In conclusion, the π band of graphene is widening when the graphene-covered area is decreasing and its intensity with respect of the substrate-derived bands is also decreasing.

A small doping (< 50 meV) is probably caused by the high density of the graphene flake edges. However, the Dirac cone is conserving its characteristic features (high electron velocity, "minigaps" caused by replicas of the cone, almost no doping) for a surface coverage up to 70% and stays easily visible on ARPES images. Our growth strategy by TPG is so a viable option. In the following chapters we will address the electronic properties of Gr/Co and Gr/Pd hybrid systems where graphene has been grown by TPG method, showing, in particular in chapter 5, that this growth process allows for a high quality of the electronic properties of the hybrids.

Chapter 5

Electronic properties of Gr/Co hybrids

This chapter presents the measurements and their analysis of the band structure of Gr/Co hybrid systems. Co being a ferromagnetic metal (FM), the induction of exchange interaction in the graphene band structure by direct hybridization may be expected.

After a quick overview of ARPES measurements of Gr/Co hybrid systems in literature, we will start by showing the band structure of the different components of the desired systems, namely Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], Co/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], in order to identify the bands corresponding to each material. In the second part we will concentrate on the electronic properties of the Co layer depending on the sample preparation conditions. Finally the effect of Co intercalation on the graphene band structure will be discussed. taken at a photon energy of 94 eV along the ΓM KΓ directions (adapted from [START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF]) and c) of Gr/Co(0001) taken at a photon energy of 62 eV (adapted from [START_REF] Trauzettel | Intact Dirac Cones at Broken Sublattice Symmetry: Photoemission Study of Graphene on Ni and Co[END_REF]).

State of the art: Gr/Co hybrids

Significant differences in the growth process have to be pointed out between literature and what is presented in chapter 4 of this manuscript. In reference [START_REF] Pacilé | Electronic structure of graphene/Co interfaces[END_REF] (fig. 5.1a)), a full graphene layer has been grown by CVD at 1030 • C, cobalt atoms were deposited at room temperature and further intercalated by an annealing in the temperature range of 600-800 K ( 330 -530 • C). In reference [START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF] (fig. 5.1b)), a high-quality graphene was obtained by cracking of propylene at 1600 K. Cobalt was then deposited at 90 K and intercalated by a stepwise annealing procedure up to 600 • C monitored by real time C 1s and Ir 4f photoelectron spectra. All the systems in these publications are complete graphene layers, suggesting an intercalation "from the top", while we use incomplete graphene to facilitate the intercalation "from the side". Moreover, it has been shown [START_REF] Drnec | Surface alloying upon Co intercalation between graphene and Ir(111)[END_REF] that an annealing at 770 K of an intercalated layer of Co between graphene and Ir(111) leads to Co and Ir intermixing and the formation of a surface alloy. Our own STM measurements have shown (chapter 4) a difference in the moiré pattern between annealing procedure at 400 • C and 500 • C. In references [START_REF] Pacilé | Electronic structure of graphene/Co interfaces[END_REF][START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF], the authors are using annealing temperatures above or at least close to this intermixing temperature.

We will now first present the ARPES measurements of Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], Co/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] in order to identify the band structure of each component of the hybrid systems. In the following we will compare the electronic structure of the Gr/Co/Ir(111) system grown with the procedure explained in chapter 4 with one grown with a recipe similar to references [START_REF] Pacilé | Electronic structure of graphene/Co interfaces[END_REF][START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF].

Electronic properties of non-intercalated systems

The identification of the band structure of each component is quite helpful in order to understand the electronic properties of the intercalated system as it will be shown in the following. As discussed in the previous chapters, Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and one ML of Co on Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] have a surface lattice parameter of 2.72 Å, Co being pseudomorphic to its substrate.

The lattice parameter of graphene is 2.45 Å. As a result of this mismatch the relative Brillouin zones (of Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Gr) although aligned do not have the same size (see fig.

5.2). We will therefore perform all the analysis in the vicinity of both K Ir and K Gr points.

Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] substrate has been cleaned in UHV environment (base pressure < 3.10 -10 We first focused our attention on the vicinity of the K Ir point. Co/Ir(111) presents a very intense state which disperses to higher energy along the M Ir K Ir direction and remains nearly flat along the K Ir Γ direction (referred as Co1 in fig. 5.3c)). Its energy at K Ir is found on the EDC to be -1.57 eV. This value does not correspond to the energy of the states of Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. The Co1 state is therefore related to the presence of the Co overlayer being a quantum well state or originating from the Co/Ir interface. A high spectral weight is also present at the Fermi level with a width of about 200 meV. Finally a weaker band (Co2) is found below -4 eV at K Ir and disperses to higher energy along both directions.

We will now focus our attention on the vicinity of K Gr point. hat, which resembles the S 3 dispersion. However, its energy is -0.99 eV at K Gr , slightly different than S 2,3 states of Ir (see fig. 5.4e)). The Co2 state remains below -4 eV at

K Gr .
Now that the Co/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] bands have been identified in the area of interest of the Brillouin zone, we will present our study of the Gr/Co(1ML)/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] system and concentrate on the induced changes of its electronic properties with respect to the non-intercalated systems.

Electronic properties of intercalated cobalt

As discussed in section 5.1, significant differences exist between our growth process and the literature and we will now compare our sample with a model sample of the published growth processes. To do so, the previously shown Co/Ir(111) sample will be used as a reference for the cobalt states. The second measured sample is a graphene layer grown by two TPG cycles covering 70% of the surface, according to AES measurement, with a ML of Co deposited and further annealed at 400 • C. This sample is representative of our growth process. For the last sample, a full graphene layer has been grown by CVD at 1100 • C and a ML of Co has been deposited at room temperature and further annealed at 650 • C. By doing so, we obtained a complete graphene layer and an intercalation achieved above the Ir-Co intermixing temperature, comparable with the previously cited papers.

In the following, these three samples will be referred as Co/Ir, Gr/Co/Ir-400 The structural quality of our samples has also been monitored by LEED measurements. of reference [START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF] before and after intercalation (fig. 5.7e),f)). Our complete graphene layer presents a very well-resolved diffraction pattern both before and after Co deposition at room temperature. This pattern is comparable with the graphene LEED pattern adapted from reference [START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF]. Upon annealing at 650 • C, some of the moiré-induced satellite spots are missing and the main spots become less resolved. The noise level is also the highest among the shown data. This degradation of the crystalline structure is also present for the Gr/Co(2ML)/Ir 600 • C sample from reference [START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF] whose LEED measurement shows only the badly resolved graphene spots which implies a disordered substrate or a fully relaxed graphene. However, our 400 • C-annealed sample shows no sign of disorder. The two main spots are still well-defined and only the noise level is slightly increasing when compared with Gr/Ir. Both the decrease of the quality of the ARPES and LEED data and the topographic changes of the sample lead to the conclusion that annealing at 650 • C induces a disordered surface alloying between iridium and cobalt. Annealing at such high temperature indeed results in Co and Ir intermixing and the formation of a surface alloy extending over a thickness of about 2-3 ML [START_REF] Drnec | Surface alloying upon Co intercalation between graphene and Ir(111)[END_REF]. This alloy has been shown to occur via a dislocation network inducing a bad crystalline quality of the final sample.

•
We saw in this section that a complete intercalation of Co results in the disappearance of the Dirac cone or at least its shift in energy around -3 eV. On the contrary, fig. 5.6 shows that, for the same amount of deposited Co, the intercalation amount increases of about a factor of 2 by increasing the annealing temperature to 500 • C. We speculate that it is possible to prepare a system composed by graphene lying on an Ir-rich Co-Ir alloy which could preserve the Dirac cone dispersion inducing only slight modifications. We therefore implemented a novel sample preparation strategy. We first partially intercalated Gr with Co at 400 • C (by depositing a low amount of Co). After further annealing at 650 • C, we promoted the formation of an Ir rich Co-Ir alloy under the graphene layer 1 . This new strategy will be further developed in the next section.

Influence on the Dirac cone

The above described sample can be obtained by deposing cobalt in the submonolayer range. We deposited 0.6 ML of Co on a 70% graphene (two TPG cycles) heated at 400 • C (sample referred as Gr/Co<1ML/Ir-400 • C in the following). Fig. 5.8 presents the ARPES measurement of this sample in the vicinity of both K Gr and K Ir (a)

M Gr K Gr Γ, b) pΓK Gr , c) M Ir K Ir Γ and d) pΓK Ir directions).
We immediately see on all four presented electronic dispersions the presence of the Dirac cone. The 3NN-TB model fitted on Gr/Ir (complete graphene layer presented in section 5.2) is displayed by red dashed lines and it well overlaps with the measured cone.

Therefore the π band of graphene is unchanged compared to Gr/Ir, suggesting that a part of graphene remains unintercalated. The Co states are also the same as Co/Ir.

Moreover, the state around -3 eV ("shifted cone") is also visible although broad and badly resolved. This band structure proves that this sample presents the coexistence of Gr/Co/Ir and Gr/Ir. Constant energy maps taken at -0.7 eV (fig. 5.8e)) shows that the 1 With Ir rich we mean with higher amount of Ir with respect to the sample measured in section 5.3 Gr/Co<1ML/Ir-400 • C with a value of 5eV.Å for M Gr K Gr direction and 5.7eV.Å for K Gr Γ direction. The measured values are consistent with literature [START_REF] Kralj | Graphene on Ir (111) characterized by angle-resolved photoemission[END_REF][START_REF] Rusponi | Highly anisotropic dirac cones in epitaxial graphene modulated by an island superlattice[END_REF].

Gr/Co<1ML/Ir-650 • C shows an important change of the cone near K Gr . The linear fits are visually different (black solid lines in by fig. 5.10c)) when compared to the ones of Gr/Co<1ML/Ir-400 • C (dashed red lines). Even if the slopes are not precisely determined for Gr/Co<1ML/Ir-650 • C, the sample shows a strong increase of the electrons velocity on both high-symmetry directions with values of about 10 eV.Å -1 (M Gr K Gr ) and 13 eV.Å -1 (K Gr Γ). This increase of electrons velocity is not consistent with a simple doping of the graphene electronic dispersion, which should result in a shift in energy of the Dirac cone.

To further characterize the modification of the band structure, constant energy maps taken at -1.5, -1.7 and -1.9 eV are displayed in fig. to reach 500 meV at 0.17Å -1 from K Gr . This variation is illustrated by constant energy maps taken at -1.5 eV and -2.2 eV (fig. 5.12a),c)) where the 3NN-TB fits are displayed with red solid lines for -1.5 and -2.2 eV respectively. In order to have the 3NN-TB model matching visually the measured data, an energy shift of +420 and +250 meV respectively is necessary, as shown by blue solid lines. Along the K Gr Γ direction, the two cones show a constant energy difference of 150 meV. The different modifications of the Dirac cone along the high-symmetry directions suggests a modification of the structural properties of the sample after the 650 • C annealing procedure.

Conclusion

In this chapter, we have shown that a ML of Co is characterized by two additional states in the area of the BZ in the vicinity of K Gr and K Ir . A first state (Co1) reaches K Ir at -1.57 eV and disperses towards higher energy along the M Ir K Ir while it remains almost flat along the K Ir Γ direction. This Co1 state, when observed near K Gr point, presents a hat-like form resembling the S 3 state of Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], and reaches K Gr at -0.99 eV. The other state (Co2) remains below -4 eV in all the measured region and is weakly intense. A high spectral weight near Fermi level is also observed. These states have been identified as 3d states in literature [START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF][START_REF] Pacilé | Electronic structure of graphene/Co interfaces[END_REF].

Co intercalation ( 1 ML), either under a complete graphene layer or a 70% graphene, keeps the Co states unchanged. However, no more Dirac cone is visible near the Fermi level. A new state (GrCo) is appearing below -3 eV, reaching K Gr at -3.3 eV. In references [START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF][START_REF] Pacilé | Electronic structure of graphene/Co interfaces[END_REF], it is identified as the π band of graphene (Dirac cone) shifted in energy by hybridization with the Co underlayer. However, within our resolution, we can not confirm that this state presents a Dirac cone-like dispersion, but only the disappearance of the cone at the Fermi level. After an annealing procedure at 650 A possible strategy to increase the induced SOC in graphene is to enhance its interaction with the substrate. However, we saw in the previous chapter 5, that a too strong interaction (175 meV/C-atom for C-Co [START_REF] Vanin | Graphene on metals: A Van Der Waals density functional study[END_REF]) can result in the destruction of the Dirac cone. In these regards, palladium is a good candidate, presenting an intermediate interaction with graphene (79 meV/C-atom for C-Pd [START_REF] Vanin | Graphene on metals: A Van Der Waals density functional study[END_REF]) and a SO strength largely superior to the one of graphene (Z P d = 46), even if smaller than Au, Pt and Ir.

This chapter will start with a short overview of the previous scientific publications about Gr/Pd. The band structures of both Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] are then analyzed to identify their own electronic dispersions. In a second time, the effect of Pd intercalation under graphene on their electronic properties is studied. A combination of angle resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM) and density functional theory (DFT) has been used to study such intercalated samples. The DFT calculations were done by Pr. Yuriy Dedkov and Pr. Elena Voloshina.

State of the art: Gr/Pd hybrids

Most of the publications studying Pd are addressing its catalytic properties and are oriented to its chemical use [START_REF] Borodzi | The kinetic model of hydrogenation of acetyleneethylene mixtures over palladium surface covered by carbonaceous deposits[END_REF][START_REF] Ho | The graphene-supported palladium and palladium -yttrium nanoparticles for the oxygen reduction and ethanol oxidation reactions : Experimental measurement and computational validation[END_REF][START_REF] Pletcher | Mesoporous palladium: the surface electrochemistry of palladium in aqueous sodium hydroxide and the cathodic reduction of nitrite[END_REF][START_REF] Moore | Sterically Demanding , Sulfonated , Triarylphosphines : Application to Palladium-Catalyzed Cross-Coupling , Steric and Electronic Properties , and Coordination Chemistry[END_REF][START_REF] Huang | Freestanding palladium nanosheets with plasmonic and catalytic properties[END_REF][START_REF] Phan | On the Nature of the Active Species in Palladium Catalyzed Mizoroki -Heck and Suzuki -Miyaura Couplings -Homogeneous or Heterogeneous Catalysis, a Critical Review[END_REF][START_REF] Toebes | Synthesis of supported palladium catalysts[END_REF]. Nevertheless, the Pd crystalline structure and electronic dispersion has also been studied both theoretically [START_REF] Östlin | Electronic structure of palladium in the presence of many-body effects[END_REF][START_REF] Drakova | Theory of scanning tunneling spectroscopy on Pd(111)[END_REF] and experimentally [START_REF] Hayashi | High-resolution angle-resolved photoemission study of electronic structure and electron self-energy in palladium[END_REF][START_REF] Ohtani | LEED Intensity Analysis of the Surface Structures of Pd(111)[END_REF][START_REF] Ilver | Angle Resolved Inverse Photoemission from Ag(111) and Pd(111)[END_REF][START_REF] Yamazaki | Angle-resolved photoemission study of Pd(110)[END_REF][START_REF] Kang | Energy dispersions and bandwidth in Pd photoemission spectra[END_REF].

Because of its high surface area and its chemical stability, graphene represents a good candidate for catalysis support. Therefore, small depositions (< 1 ML) of Pd on top of a graphene layer have been widely studied in order to obtain a Pd decorated graphene layer used as a two-dimensional reactive platform. The structure of such small depositions have been theoretically studied for a single Pd adatom and dimers [START_REF] Thapa | Palladium atoms and its dimers adsorbed on graphene : First-principles study[END_REF] and small clusters [START_REF] Cabria | Theoretical study of the transition from planar to three-dimensional structures of palladium clusters supported on graphene[END_REF] (< 10 atoms). The adsorption of Pd adatoms on graphene has been found to be stable for a single adatom on an atop site and for dimers on bridge sites [START_REF] Thapa | Palladium atoms and its dimers adsorbed on graphene : First-principles study[END_REF]. However the growth of 3D clusters appears to be favored from 5 Pd adatoms deposition [START_REF] Cabria | Theoretical study of the transition from planar to three-dimensional structures of palladium clusters supported on graphene[END_REF].

The deposition of well-dispersed Pd nanoparticles on graphene has been achieved [START_REF] Jin | Decoration , Migration , and Aggregation of Palladium Nanoparticles on Graphene Sheets[END_REF].

These nanoparticles are stable up to 800 • C were they agglomerate in larger particles.

Focusing on the effect of Gr/Pd interfaces, the growth of graphene layer on bulk Pd (for both Pd [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Pd(100) surfaces) has first been achieved by carbon segregation [START_REF] Hamilton | Carbon segregation to single crystal surfaces of Pt[END_REF][START_REF] Murata | Orientation-dependent work function of graphene on Pd (111)[END_REF][START_REF] Gao | Controllable growth of single-layer graphene on a Pd (111) substrate[END_REF]. This growth method has been shown to result in six different rotational domains (see fig. 6.1a)), each one of them corresponding to a variation of the work function [START_REF] Murata | Orientation-dependent work function of graphene on Pd (111)[END_REF], even though single-oriented graphene has also been achieved [START_REF] Gao | Controllable growth of single-layer graphene on a Pd (111) substrate[END_REF]. Moreover, a millimeter-scale single-oriented graphene layer has recently been grown by segregation on an amorphous Pd silicide film [START_REF] Kim | Millimeter-Scale Growth of Single-Oriented Graphene on a Palladium Silicide Amorphous Film[END_REF] (see fig. 6.1b)). The amorphicity of the Pd silicide film indeed promotes the uniformity of the graphene layer, as shown in fig. 6.1b) where only the six Gr spots are visible, but only weak interactions between graphene and the underneath film have been measured.

Graphene has also been grown epitaxially on bulk palladium by CVD [START_REF] An | Large-Area Synthesis of Graphene on Palladium and Their Raman Spectroscopy[END_REF][START_REF] Kwon | Growth of Semiconducting Graphene on Palladium[END_REF]. This The graphene flake is extending over few micrometers and grow continuously over Pd terraces (adapted from [START_REF] An | Large-Area Synthesis of Graphene on Palladium and Their Raman Spectroscopy[END_REF]). b) Small scale SEM image of Gr/Pd showing the typical nucleation sites for graphene growth (adapted from [START_REF] An | Large-Area Synthesis of Graphene on Palladium and Their Raman Spectroscopy[END_REF]). c) STM image of the moiré pattern of Gr/Pd (adapted from [START_REF] Kwon | Growth of Semiconducting Graphene on Palladium[END_REF]).

growth is self-limiting and results in large high-quality graphene layer (fig. 6.2a)). The nucleation of graphene is mostly located at the atomic terrace steps [START_REF] An | Large-Area Synthesis of Graphene on Palladium and Their Raman Spectroscopy[END_REF] (fig. 6.2b)).

A strong interaction has been found between Pd and graphene (fig. 6.2c)), opening a band gap in the graphene band structure [START_REF] Kwon | Growth of Semiconducting Graphene on Palladium[END_REF]. These results have been theoretically confirmed by local-density approximation (LDA) [START_REF] Vanin | Graphene on metals: A Van Der Waals density functional study[END_REF], finding a C-Pd distance of 2.33 Å and an interaction of 79 meV/C-atom.

The intercalation of Pd under graphene has not been largely addressed by the scientific community. It has been reported only for few systems, namely on Gr/Ru(0001) [START_REF] Huang | Intercalation of metal islands and films at the interface of epitaxially grown graphene and Ru (0001) surfaces[END_REF] and Gr/SiC(0001) [START_REF] Yagyu | Neutralization of an epitaxial graphene grown on a SiC (0001) by means of palladium intercalation[END_REF] surfaces. In both cases, the graphene is undisturbed by the intercalated layer and a moiré pattern is observed by STM (fig. 6.3). In the case of In summary, Pd is mostly studied for its catalytic properties, specially on top of graphene used as a support. Gr has been grown on bulk Pd by both segregation and CVD methods.

Pd has also been intercalated under Gr for few substrates. However, we did not find any publications about the spectroscopic study of such Pd-intercalated Gr hybrid systems.

Electronic properties of Pd/Ir(111)

As already seen in the previous chapter the identification of the different bands of the constituents of the hybrid system is quite helpful for the understanding of the overall electronic properties. In this section we therefore present the ARPES measurements of Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] substrate has been prepared in UHV environment (base pressure < 3.10 111) band structure calculated by DFT (adapted from [START_REF] Pletikosić | Photoemission and density functional theory study of Ir(111); Energy band gap mapping[END_REF]). e) Schematic representation of the BZ of both Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. The right part is a zoom around the K points of the system and describes the four cuts which will be used to present ARPES data.

In the following we will present the electronic dispersion of Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. were performed with the Vienna ab initio simulation package (VASP) [START_REF] Kresse | Norm-conserving and ultrasoft pseudopotentials for firstrow and transition elements[END_REF][START_REF] Kresse | Software vasp, vienna[END_REF]. The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional was employed [START_REF] Perdew | Generalized gradient approximation made simple[END_REF].

The electron-ion interaction was described within the projector augmented wave (PAW) method [START_REF] Blöchl | Projector augmented-wave method[END_REF] with C (2s, 2p), Ir (5d, 6s) and Pd (4d, 5s) states treated as valence states.

The BZ integration was performed on Γ-centered symmetry reduced Monkhorst-Pack meshes using a Methfessel-Paxton smearing method of first order with σ = 0.15 eV, except for the calculations of total energies. For those calculations, the tetrahedron method with Blöchl corrections [START_REF] Blöchl | Improved tetrahedron method for brillouin-zone integrations[END_REF] was used. The k mesh for sampling the supercell Brillouin zone are chosen to be as dense as at least 24x24, when folded up to the simple graphene unit cell. Dispersion interactions were considered by adding a 1/r 6 atom-atom term as parameterized by Grimme ("D2" parameterization) [START_REF] Grimme | Semiempirical gga-type density functional constructed with a longrange dispersion correction[END_REF]. The spin-orbit interaction is taken into account. The supercell used in this work is constructed from a slab of six layers of metal, a graphene layer adsorbed on one (top) side of a metal slab and a vacuum region of approximately 20 Å. The used supercell has a (10 × 10) lateral periodicity with respect to the graphene layer and (9 × 9) periodicity with respect to the unit cell of the Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] surface. The lattice constant in the lateral plane was set according to the optimized value of bulk metal (a Ir(111) = 2.723 Å yielding a gr = 2.451 Å).

The positions (x, y, z-coordinates) of C atoms and intercalant as well as z-coordinates of the two topmost layers of a substrate were fully relaxed until forces became smaller than 0.02 eVÅ -1 . The band structures calculated for the studied systems were unfolded to the graphene (1x1) and the respective Ir( 111) substrate (1x1) primitive unit cells according to the procedure described in [START_REF] Medeiros | Effects of extrinsic and intrinsic perturbations on the electronic structure of graphene: Retaining an effective primitive cell band structure by band unfolding[END_REF][START_REF] Medeiros | Unfolding spinor wavefunctions and expectation values of general operators: Introducing the unfoldingdensity operator[END_REF] with the code BandUP. Such situation, together with the expected strong graphene-Pd interaction [START_REF] Vanin | Graphene on metals: A Van Der Waals density functional study[END_REF], makes Pd single layer on Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] extremely appealing to induce spin-orbit coupling in the graphene. The electronic properties of such Gr/Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] samples will now be addressed in the next section.

Electronic properties of intercalated palladium

As mentioned in chapter 2, since the high quality growth of well aligned graphene requires typically high temperatures at which single atomic layers on metals are normally not stable, we proceeded by intercalation to reach the desired system. To promote Pd intercalation, the graphene layer has been grown by TPG up to a coverage of 85% (3 cycles) determined by AES. The Pd deposition of one ML has been done at 400 Upon Pd intercalation, strong modifications of the system band structure with respect to Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] are immediately evident. The band dispersion along the M Gr K Gr Γ direction of the BZ can be analyzed considering three energy regions in which several electronic states are present. The first one from -1.5 to -0.7 eV presents hole like dispersing states with apex at the K Gr point at -0.7 eV, a second one from -0.5 to -0.3 eV shows a rather flat sets of states that traverse the reciprocal space, and finally a high electronic density can be found at the Fermi level located at K Gr . It is evident that in the first two energy regions the electronic states present a rather complex band dispersion. In the following we will demonstrate that those states are in fact composed by two spin-polarized components. For this purpose we show three energy distribution curves in fig. 6.7c) (black dashed lines) corresponding to the momentum highlighted by the three white arrows in fig.

6.7b). From the comparison of these curves it is evident that the hole-like dispersing state has indeed two components. Although the same analysis is more difficult for the low dispersing state in the second energy region, we identified a two-states structure along the M Gr K Gr far from the K Gr point (see profile I in fig. 6.7c)). In order to quantitatively evaluate the presence of a doublet of electronic states we fitted the EDCs, in the momentum region highlighted by the red dashed lines in fig. This analysis of our ARPES measurements demonstrates that graphene hybridizes with the two Pd QWSs giving rise to a complex band structure constituted of three pockets, located at different energies. Two of such pockets are indeed composed by two split electronic states. The energy separation inside the low energy pocket results to be momentum dependent increasing far from the K Gr point up to more than 200 meV.

Such a behavior suggests that induced spin-orbit interaction in graphene, due to Pd intercalation, could be accounted for the energy splitting.

In order to prove this scenario we performed DFT simulations, with considering spinorbit coupling, of Gr/Pd/Ir(111) compared with both Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Pd/Ir(111) (fig.

6.8). According to the present results, graphene in Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] is weakly p-doped and the sizeable band-gap is opened for the valence band states directly above E F as a result of hybridization of the graphene π and Ir 5d z 2 valence band states (fig. 6.8a)). Due to the relatively large average distance between Gr and Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] the induced spin-orbit interaction for the graphene π electrons is weak that leads to the small spin-splitting of the π band in the vicinity of E F of only 20 meV [START_REF] Voloshina | Realistic Large-Scale Modeling of Rashba and Induced Spin -Orbit Effects in Graphene / High-Z-Metal Systems[END_REF].

The intercalation of Pd in Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] complicates the electronic structure of the resulting system (fig. 6.8c)). However, the dispersion of the graphene π bands in the vicinity of the K Gr point can still be clearly recognized allowing the analysis of the spin topology of the valence band states. As can be seen, graphene is n-doped in Gr/Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] thus its doping is reversed compared to the one of the parent system. The interesting feature of Gr in the formed intercalated system is the evolution of band gaps in the electronic spectrum of Gr. First of all, the large band gap for graphene π states in Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] which is located directly above E F is closed meaning that the Pd layer blocks the effective hybridization of the valence band states of Gr and Ir. Secondly, a "huge" band gap of 600 meV is opened for the graphene π states directly at the K Gr point. Also the lower branch of the graphene π band becomes strongly spin-polarized, structure of the Gr/Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Pd/Ir(111) systems unfolded on the Brillouin zone corresponding to the Ir(111) substrate lattice (fig. 6.9a) and c)). One can see that the band gap in the electronic spectrum of the Gr π states appears as a result of the "avoid crossing" mechanism due to the Pd 4d z 2 states. In its turn the respective Pd band is a QWS which is formed in the Pd layer sandwiched between a Gr layer and the Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] substrate, as discussed in section 6.2. This state can be also recognized in the band structure of the intermediate system -Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] -where it appears in the energy-kvector window of the electronic structure of the Ir(111) slab which is located around the K Ir point. As can be also seen this state is strongly spin-polarized due to the large spin-orbit interaction in Pd. The respective interaction between Gr and Pd layer at the relatively short distance between two layers of 2.363 Å leads to the appearance of the corresponding induced spin-orbit splitting of the Gr π bands as was discussed earlier.

M Ir ← K Ir → Γ 0 1 -1 -2 -3 E-E F (eV) M Gr ← K Gr → Γ 0 1 -1 -2 -3 E-E F (
M Gr ← K Gr → Γ 0 1 -1 -2 -3 E-E F (eV) M Gr ← K Gr → Γ 0 -0.5 -1 -1.5 M Gr ← K Gr → Γ 0 -0.5 -1 -1.5 E-E F (eV) E-E F (
DFT simulations allow us to point out two key ingredients of the Gr/Pd/Ir(111) system.

What we identified as the split low energy pocket in the ARPES experiments is indeed the modified graphene π state which is strongly p-doped and spin-polarized. The high spectral weight measured at K Gr at the Fermi level corresponds to the π * graphene state showing therefore the opening of a large bandgap (600 meV) in the graphene band structure.

Conclusion

In this chapter, we have shown that a Pd ML grows pseudomorphic to the Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] substrate. Its electronic dispersion is characterized by two QWSs which present an energy splitting going from 120 meV at K Gr to 170 meV at K Ir . DFT calculations confirm that these two states are spin-polarized due to Pd SOC. These two spin-polarized states are located in the vicinity of the Dirac cone of graphene. Once Pd is intercalated between Gr and Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], the Dirac cone electronic dispersion is indeed strongly modified.

The graphene results strongly n-doped with the opening of a 600 meV bandgap at the K Gr point. Moreover the π state results spin-polarized with momentum dependent energy splitting that goes from 200 meV at 0.15 Å -1 from K Gr and is strongly reduced approaching K Gr . These results are strongly supported by DFT calculations which demonstrate that the leading mechanism for the spin polarization of the Dirac cone is indeed intrinsic SOC induced by electronic hybridization between graphene and the intercalated Pd layer.

The analysis performed in this chapter leads to two fundamental conclusions. First of all, the graphene-Pd system is an appealing template for the realization of spintronics devices and for the study of novel quantum phases due to the induced spin-polarization of the Dirac cone. More generally, the proposed approach on the tailoring of the dimensionality of heavy materials interfaced with a graphene layer might lead to the induced giant spinorbit splitting of the graphene valence band states. In fact spin-polarized quantum well states exist in several other systems [START_REF] Altmann | Spin-polarized quantum well states[END_REF][START_REF] Yee | Spin-polarized quantum well states on Bi 2-x Fe x Se 3[END_REF][START_REF] He | Spin Polarization of Quantum Well States in Ag Films Induced by the Rashba Effect at the Surface[END_REF][START_REF] Kormondy | Large positive linear magnetoresistance in the two-dimensional t 2g electron gas at the EuO / SrTiO 3 interface[END_REF] and might exist for other single atomic layers on surfaces. If graphene hybridizes with such QWSs the induced spinseparation in the Gr valence band could be even stronger than what reported here.

Chapter 7

Preliminary study of electronic properties of Gr/CoPd hybrids

We saw in the previous chapters that both Co and Pd have an effect on the graphene band structure. Intercalated Co, under certain growth conditions, induces an enhancement of the Fermi velocity. Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] presents two QWSs spin-split by SOC. These states hybridize with the Dirac cone of graphene, resulting in the opening of a 600 meV bandgap and the spin-polarization of the graphene π state. In this chapter, we present our preliminary study on the co-intercalation of Co and Pd under graphene to address the possibility of a further modification of the graphene band structure. A first section will present a quick overview of Co-Pd systems. After a structural study, we will then present our ARPES measurements of such Gr/Co-Pd systems. This chapter presents preliminary results and further experiments and analysis are required for a full understanding of Gr/Co-Pd/Ir systems.

State of the art

This section is focusing on scientific publications about two subjects: the Pd-Co systems and the multi-component intercalation under graphene. We will first address the structural and electronic properties of PdCo systems, with a particular attention on their surfaces. The multi-component intercalation will then be discussed.

State of the art: CoPd systems

As seen in chapter 6, Pd presents great catalytic properties. A huge effort has been made to optimize the efficiency of Pd catalysts, specially by alloy formation with other materials. For this chemical purpose, CoPd alloy nanoparticles have been grown on several substrates [START_REF] Wang | Pt-Decorated PdCo at Pd / C Core -Shell Nanoparticles with Enhanced Stability and Electrocatalytic Activity for the Oxygen Reduction Reaction[END_REF][START_REF] Vondrova | Supported Superparamagnetic Pd / Co Alloy Nanoparticles Prepared from a Silica / Cyanogel[END_REF][START_REF] Kuttiyiel | Gold-promoted structurally ordered intermetallic palladium cobalt nanoparticles for the oxygen reduction reaction[END_REF][START_REF] Carlsson | The Structure and Reactivity of Al 2 O 3 -Supported Cobalt -Palladium Particles : A CO-TPD , STM , and XPS Study[END_REF], mostly for the oxygen reduction reaction (ORR).

While theoretical calculations predict a Co-core Pd-shell structure for clusters up to 50 atoms with a 1:1 composition [START_REF] Arslan | Theoretical study of the structures and chemical ordering of cobalt -palladium nanoclusters[END_REF] (see fig. 7.1a)), the experimental study of the sequential deposition of Pd and Co on an Al 2 O 3 substrate shows that the first deposited element forms the core while the second forms the shell [START_REF] Carlsson | The Structure and Reactivity of Al 2 O 3 -Supported Cobalt -Palladium Particles : A CO-TPD , STM , and XPS Study[END_REF]. These core-shell structures can also include other material like AuPd shell [START_REF] Kuttiyiel | Gold-promoted structurally ordered intermetallic palladium cobalt nanoparticles for the oxygen reduction reaction[END_REF] or Pt decorated-Pd core [START_REF] Wang | Pt-Decorated PdCo at Pd / C Core -Shell Nanoparticles with Enhanced Stability and Electrocatalytic Activity for the Oxygen Reduction Reaction[END_REF]. The core-shell structure is temperature-dependent and becomes a random alloy above 500 • C [START_REF] Kim | Phase change of bimetallic PdCo electrocatalysts caused by different heat-treatment temperatures : Effect on oxygen reduction reaction activity[END_REF].

Focusing on PdCo films, which is the aim of this work, we first analyze the surface of the bulk PdCo alloy which has been widely studied [START_REF] Bagguley | Ferromagnetic resonance in a series of alloys : II . Binary alloys of cobalt with platinum and palladium , and one iron-palladium alloy Ferromagnetic resonance in a series of alloys 11 . Binary alloys of cobalt with platinum and palladium , and one ironpalladium alloy[END_REF][START_REF] Ishida | The Co-Pd ( Cobalt-Palladium ) System[END_REF][START_REF] Bidwell | The thermodynamic properties of Cobalt-Palladium solid solutions[END_REF][START_REF] Takahashi | Measurement of magnetostriction constants in polycrystalline alloy and multilayer films of PdCo and PtCo[END_REF][START_REF] Matsuo | Ordered alloys in the Cobalt-Palladium systems[END_REF][START_REF] Shamsuddin | Thermodynamics of dilute solutions of hydrogen in PdNi, PdCo, and PdFe alloys[END_REF][START_REF] Niessen | Enthalpies of formation of liquid and solid binary alloys based on 3d metals[END_REF].

Depending on the alloy composition, width and temperature, different structures have been found [START_REF] Ishida | The Co-Pd ( Cobalt-Palladium ) System[END_REF][START_REF] Matsuo | Ordered alloys in the Cobalt-Palladium systems[END_REF] (see fig. 7.1b)). An extensive thermodynamic study of PdCo alloy has also been realized [START_REF] Niessen | Enthalpies of formation of liquid and solid binary alloys based on 3d metals[END_REF][START_REF] Bidwell | The thermodynamic properties of Cobalt-Palladium solid solutions[END_REF][START_REF] Shamsuddin | Thermodynamics of dilute solutions of hydrogen in PdNi, PdCo, and PdFe alloys[END_REF], with a predicted heat of mixing for the 1:1 composition of -1 kJ.mol -1 [START_REF] Niessen | Enthalpies of formation of liquid and solid binary alloys based on 3d metals[END_REF]. This value is varying with the alloy composition, going from endothermic for Co rich alloys to exothermic for Pd-rich alloy [START_REF] Bidwell | The thermodynamic properties of Cobalt-Palladium solid solutions[END_REF]. The study of the surface composition of bulk PdCo has revealed [START_REF] Krawczyk | Surface Composition of the CoPd Alloys Studied by Electron Spectroscopies[END_REF] that Pd segregates above 300 • C for alloy composition of Pd > 50%, consistently with the lower value of Pd surface free energy (2100 mJ.m -2 ) with respect to the one of Co (2550 mJ.m -2 ).

The segregation effect has also been theoretically studied, giving surface energies of 0.824 eV/atom for Pd [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and 0.961 eV/atom for Co(0001) surfaces [START_REF] Vitos | The surface energy of metals[END_REF] and surface segregation energies of 0.29 eV for Co in Pd and -0.6 eV for Pd in Co [START_REF] Ruban | Surface segregation energies in transitionmetal alloys[END_REF]. In the context of the ORR catalysis, CoPd alloy and Pd-skin CoPd alloy surfaces and their structural and electronic properties have been studied. Co presence in Pd [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] surface leads to a small lattice contraction, for example going from 3.89 Å to 3.85 Å for the P d 0.75 Co 0.25 [START_REF] Lamas | Surfaces : An ab Initio Comparative Study[END_REF][START_REF] Son | Effects of Co Content in Pd-Skin / PdCo Alloys for Oxygen Reduction Reaction : Density Functional Theory Predictions[END_REF]. The enthalpy of mixing for increasing Co proportions, compared with the phase-separated Pd-skin system at 60%, shows that the most stable composition is P d 0.7 Co 0.3 [START_REF] Son | Selectivity of Palladium -Cobalt Surface Alloy toward Oxygen Reduction Reaction[END_REF] with an octahedral-like structure (see fig. for Pd [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF].

The interaction of Co and Pd has recently been studied in multi-layers systems. Among several observed emerging electronic features of such layered systems, we can cite current induced spin-orbit torques [START_REF] Jamali | Spin-Orbit Torques in Co / Pd Multilayer Nanowires[END_REF], enhancement of the magnetic anisotropy [START_REF] Smith | Magnetization reversal and magnetic anisotropy in patterned Co / Pd multilayer thin films multilayer thin films[END_REF] and stable Néel skyrmions [229]. However, the typical width of a layer in this kind of system is above 1 nm, far from our objective of one monolayer.

State of the art: multi-component intercalation under graphene

Multi-metallic intercalation under graphene has not been widely studied. We found only one publication showing a multi-component intercalation under graphene [START_REF] Bazarnik | Multi-layer and multicomponent intercalation at the graphene/Ir(111) interface[END_REF]. In this work, successive deposition of first Fe and second Co is performed on a Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] sample (see fig. To summarize, CoPd alloys present a large variety of structures depending on the temperature, the alloy composition and the dimensionality (bulk, surface, nanoparticles).

However, Pd seems to be located preferably near the surface due to its lower free surface energy. For low-dimensional systems (nanoparticles), a core-shell structure is favored below 500 • C. The composition of the core-shell structure is predicted to be Pdshell/Co-core but the inversed composition has been observed by successive deposition of Pd and Co. In the alloy, Pd and Co show electronic interaction with the hybridization of their d-bands. More complex interactions are observed for Co-Pd multi-layered systems. With these insights, we can expect that the successive intercalation of Co and Pd, at temperatures below 500 • C, will produce core-shell nanostructures. On the contrary it is possible that, due to the low mobility of atoms once intercalated, the co-intercalation of Co and Pd results in an alloy formation without phase separation.

Structural study

We will now address the structural properties of both Co and Pd intercalated systems.

The presented results are preliminary studies and do not draw a full picture of the system.

Co 0.5 ML -500x500 nm 2 100x100 nm 2 In chapter 4, we saw that 0. No other feature is observed in these LEED patterns, which are identical to the one of Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Gr/Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], except for a slight reduction of the signal to noise ratio.

The crystalline quality of the sample after the co-deposition of Pd and Co is therefore comparable with the previously studied sample.

Preliminary ARPES experiments

We will now focus our attention on the electronic properties of Gr(70%)/Pd(80%)-Co(20%) and Gr(70%)/Pd(70%)-Co(30%) samples in an energy range up to -1.5 eV below the Fermi level, as in chapter 6. These are compared to Gr(85%)/Pd which was presented in the previous chapter and to Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. Fig. 7.8 displays the electronic dispersion along the M Gr K Gr Γ direction of these four samples, measured with a photon energy of 21.22 eV (HeI) and at 50 K (liquid helium). The incident light polarization is varying and is precised in the legend.

We saw in chapter 5 that Co is mostly characterized by an electronic state with a hat-like shape along the M Gr K Gr Γ direction, reaching -0.99 eV at K Gr . None of the co-deposited samples shows the presence of this Co1 state, up to 0.3 ML deposition of Co.

Regarding the Pd-derived electronic states, the Gr(70%)/Pd(80%)-Co(20%)/Ir(111) sample (fig. 7.8d)) shows the hole-like split states reaching K Gr at -0.7 eV that DFT calculations identified as the spin-polarized π band of graphene in chapter 6, as for Gr/Pd/Ir (fig. 7.8b)). However, within our resolution, these states are less defined and their shape seems slightly different. Moreover, the second pocket of spin-polarized states around -0.3 eV observed for Gr/Pd/Ir is not retrieved. In the high-energy region (> -0. ARPES measurement of the Gr(70%)/Pd(70%)-Co(30%)/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] sample was realized with s-polarized incident light. This data (fig. 7.8e)) is compared with Gr/Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] also measured with a s-polarization (fig. 7.8c)). In these experiment conditions, Gr/Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] shows the split states around -0.3 eV with the same intensity as for p-polarization, while the spin-polarized π band of graphene around -0.7 eV is less defined. Upon 30% Co deposition, the split states around -0.3 eV are no longer visible and a broad weakly intense state is observed around -0.7 eV at K Gr . The resolution of this state is worse than both Gr/Pd/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] taken with the same polarization and the Gr(70%)/Pd(80%)-Co(20%)/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] sample (p-polarization).

In conclusion, a small amount of co-deposited Co (20%) induces a modification of the Pd-derived electronic states with the disappearance of the two spin-polarized split states around -0.3 eV at K Gr . In this energy region, two new linear dispersing states appear and they are not well described by the 1NN-TB fit of graphene. Further experiments in a larger energy range, for different alloy compositions and experimental conditions, are required to properly address the effect of Pd and Co co-deposition on the graphene band structure.

Chapter 8

Conclusions and perspectives

Nowadays, one of the key challenge for the integration of graphene in active elements for spintronics is the spin-polarization of its Dirac cone. This situation can be promoted in graphene by inducing spin-orbit coupling or exchange interaction. One of the best ways to modify the graphene electronic dispersion is to interface it with other materials with desired properties. The aim of this thesis is to present a spectroscopic study of graphene based hybrid systems where the graphene layer is interfaced with two promising materials: Cobalt and Palladium. These are expected to induce respectively exchange interaction and spin-orbit coupling in the graphene layer.

The graphene/metal hybrid systems were realized in situ in an UHV environment by means of intercalation of a single metallic layer between graphene and its Ir(111) substrate. Our study on the intercalation of Co, performed by STM, shows that the structure of the hybrid system is strongly temperature dependent with the formation of a Co/Ir alloy under graphene if the system is heated higher than 500 • C.

To enhance the efficiency of the intercalation process, we prepared a graphene layer with a high density of nanometric holes by Temperature-Programmed Growth. The intercalation of Co and Pd has then been achieved via a deposition at 400 • C taking advantage from the intercalation "from the side" of the graphene flake. Co atoms are shown to be energetically favored under graphene, reaching a complete intercalation with no remaining Co on Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. On the contrary, the energy landscape for Pd atoms seems to be rather flat showing both intercalation under graphene and the formation of 2D islands on Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. However, a complete intercalation of the graphene layer can be ensured by a 1 ML deposition of Pd.

To estimate the effect of flake edges on the graphene band structure, ARPES measurements of TPG-grown graphene are compared to the ones of a complete graphene layer.

We show that a small doping (< 50 meV) is caused by the flake edges. Otherwise, the Dirac cones conserves all its characteristic features. Only the quality of the photoemission data is slightly decreasing (increase of the bands width) with the surface coverage.

We first addressed the electronic properties of Gr/Co hybrid system. Our study reveals that the structural quality of the Co layer depends on the growth conditions. If the intercalation temperature is higher than the Co-Ir alloy formation temperature, the Co bands result indeed wider and less defined. Nevertheless, independently of the preparation conditions, if Gr is lying on Co, the Dirac cone structure close to the Fermi level is destroyed.

We managed to prepare a Gr/Co hybrid which preserves the Dirac cone dispersion. It has been done by depositing a low amount of Co and inducing Co-Ir intermixing with high temperature annealing (650 • C). This system presents a strong modification of the Dirac cone, which is momentum-dependent along the M Gr K Gr direction while it is constant along the K Gr Γ direction. The electrons velocity at the Fermi level is increasing by a factor of about 2, with respect to Gr/Ir [START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF].

In Gr/Pd hybrid systems, we achieved a spin-splitting of 200 meV in graphene electronic dispersion by its interaction with QWSs of Pd/Ir. The hybridization of graphene with such spin-polarized states, results in the opening of a 600 meV bandgap and in the momentum-dependent spin-polarization of the graphene Dirac cone. The experimental data are well supported by DFT calculations taking spin-orbit interaction into account.

These results demonstrate that graphene-Pd system is an appealing template for the realization of spintronics devices and, more generally, they pave the way for the use of quantum well states for the band engineering of graphene.

We then attempted a preliminary study of the electronic properties of Gr/CoPd hy- We first define x, y, and z the axis of reference as displayed in fig. A.1: z is orthogonal to the incidence plane of the analyzer, x parallel to this plane and horizontal, y parallel to this plane and vertical. In a first approximation, the entrance slit of the analyzer is considered as a one-dimensional vertical line. Therefore, the only photoemitted electrons entering this slit are those with a null x component. In the reference system, an electron is reaching the analyzer if its normalized wave vector has the form: In the same way, after both θ and φ rotations, the unit vector of the ψ rotation axis has become:

u k =      
u ψ (θ, φ) = R φ R θ u z = R φ R θ       0 0 1       =      
sin θ(cos 2 θ(2 cos φ -1) + sin 2 θ)

cos θ sin φ cos θ(cos 2θ cos φ + 2 sin 2 θ)

      (A.7)
, and the ψ rotation matrix is:

R ψ (θ, φ, ψ) = R(ψ, u ψ ) (A.8)
We are not showing the final result for convenience.

Once we obtain the three rotation matrices, the unit vectors of the sample surface ( x S , y S ) are:

x S = R ψ R φ R θ u x (A.9a)

y S = R ψ R φ R θ u y (A.9b)
, and we can project the entering wave vector onto these unit vectors:

k x ∝ u k . x S =       0 sin ϕ cos ϕ       R ψ R φ R θ       1 0 0       (A.10a) k y ∝ u k . y S =       0 sin ϕ cos ϕ       R ψ R φ R θ       0 1 0       (A.10b)
We finally add the energy dependence as discussed in section 3. For the central pixel of the analyzer (ϕ = 0), we measure the point Γ(0, 0) of the reciprocal space. We define the k x and k y axis of the reciprocal space so that k x corresponds to the ΓK direction of the graphene Brillouin zone, and k y the orthogonal axis passing through the Γ point. The measured line is centered on the Γ point and has an angle of ψ with the k y axis. We define ψ = 0 the angle so that the measured line is vertical in After a scan at a fixed θ, we obtain an intensity matrix I(ϕ, E) which becomes I(θ, ϕ, E) after a serie of regularly spaced θ. We can then transform each triplet (θ, ϕ, E) in (k x , k y , E) to obtain I(k x , k y , E). However, θ has a constant step (chosen by the user)

and so have ϕ and E (pixels of the analyzer), which is very convenient for further data treatment. The transformation from angles to reciprocal space is not linear and will result in a (k x , k y , E) discrete space with varying steps. Therefore, we first calculate the extremal values for the complete data set of k x , k y and E. A constant step for each of these three dimensions, i.e. the size of a voxel (3D pixel), has now to be determined.

The transformation from angles to wave vectors is made in constant energy planes, so we can keep the same energy step as the analyzer. For HeI and HeII wavelengths, we choose respectively 3 meV and 10 meV. These δE values are not corresponding to the energy resolution but only to the size of a voxel in the energy dimension.

For the (k x , k y ) plane, we have to determine the largest experimental δk obtained within our experimental conditions. For convenience, we choose to take the same step for both k x and k y dimensions. Both k x and k y evolve with ∝ √ E kin , so the maximal δk will be found at the highest energy. The value of δk is then depending on both ϕ and θ.

Concerning ϕ, the analyzer has 1040 pixels devoted to the 30 , reaching values of 0.006 Å -1 and 0.019 Å -1 for HeI and HeII respectively. k y is not depending on θ, so no δk y is caused by the δθ step. The chosen δk for the voxel size must be higher than the experimental δk, so that no empty voxel emerges from the data transformation in the reciprocal space. Therefore, we choose δk = 0.01 Å

Ir( 111 )

 111 (K Ir ). Un cryostat à flux permet de refroidir l'échantillon à une température estimée à 50 K (hélium liquide) ou supérieure à 70 K (azote liquide). La représentation des données d'ARPES est ensuite expliquée. Toutes les coupes 2D présentées dans la suite de ce travail sont illustrées, ainsi que la représentation par des courbes de distribution en énergie (en anglais, energy distribution curve, EDC) ou en vecteur d'onde (en anglais, momentum distribution curve, MDC). Les deux procédures expérimentales utilisées dans ce travail, correspondant aux énergies incidentes HeI et HeII, sont détaillées. Le chapitre 4 présente l'étude de croissance et des propriétés structurales des systèmes hybrides Gr/Co/Ir et Gr/Pd/Ir. Cette étude à été réalisée à l'université de Constance (Allemagne) en collaboration avec le Pr. Mikhail Fonin, lors d'un séjour d'un mois. La croissance de tels systèmes hybrides est composée de plusieurs étapes : une couche de graphène est tout d'abord construite sur le substrat Ir(111), et une monocouche atomique (Co ou Pd) est ensuite intercalée entre le graphène et le substrat. L'étude des propriétés structurales à chacune des étapes est réalisée par des mesures topographiques de microscopie à effet tunnel (STM).

  Tout d'abord, une étude plus détaillée des échantillons intercalés de CoPd doit être réalisée avec la recherche de leur structure et de leurs propriétés électroniques en fonction de la composition de l'alliage. L'effet de l'augmentation de la température devrait également être abordé.Notre étude des hybrides Gr/Co a révélé le rôle clé de la température d'intercalation sur les propriétés structurales et électroniques du système avec la formation d'un alliage Co-Ir, sous le graphène, qui fournit une modification du cône de Dirac dépendante du vecteur d'onde. Une étude approfondie de l'effet de l'alliage de surface Co-Ir sur la dispersion électronique du graphène doit être effectuée, grâce à une analyse plus détaillée des propriétés électroniques d'hybrides en fonction de la structure et de la composition de l'alliage. De plus, une fois l'alliage Co-Ir formé, l'intercalation ultérieure de Pd pourrait modifier l'interaction de celui-ci, entraînant une dispersion électronique différente.

Chapter 3 Chapter 4

 34 presents a brief introduction to the main techniques used to characterize the Gr-based hybrid systems. These are Scanning Tunneling Microscopy (STM) and Angle-Resolved Photoemission Spectroscopy (ARPES). The first one provides information about the morphology and the organization of the hybrid surfaces. The second one provides information on the occupied band structure of the surface of the sample. After the description of the basic principles of STM and ARPES, the experimental set-up is presented. It consists in a UHV chamber specifically designed to grow in situ and to perform spectroscopic characterization of two-dimensional systems. The daily experimental procedure it then briefly resumed. A more detailed explanation of the data treatment is given in appendix A. presents the structural study of Gr-based hybrid systems, mostly by means of STM experiments.

Figure 2 . 1 :

 21 Figure 2.1: a) Simulated band structure of graphene in its first Brillouin zone. The inset is a zoom on one of the Dirac cone (adapted from [17]). b) Schematic representation of the BZ of graphene.

Figure 2 . 2 :

 22 Figure 2.2: Schematic representation of the graphene hexagonal lattice (lattice constant a = 2.461 Å) (adapted from [88]).

Figure 2 . 3 :

 23 Figure 2.3: a) Ab initio (full line) and 1NN-TB (dashed line) dispersions of graphene, with ε 2p = s 0 = 0 and γ 0 = -2.7 eV. Bottom: difference ∆E between the two dispersions. b) Ab initio (full line) and 3NN-TB (dashed line) dispersions of graphene, with ε 2p = -0.28 eV, s 0 = 0.073, γ 0 = -2.97 eV, s 1 = 0.018, γ 1 = -0.073 eV, s 2 = 0.026 and γ 2 = -0.33 eV. Bottom: difference ∆E between the two dispersions (adapted from [88]).

  induced band gap opening. A first promising candidate for a substrate opening a band a

Figure 2 . 4 :

 24 Figure 2.4: ARPES measurements at K point for a) Gr/SiC (adapted from[START_REF] First | Substrate-induced bandgap opening in epitaxial graphene[END_REF]), b) Gr/hBN (adapted from[START_REF] Wang | Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride[END_REF]), c) Gr/Cu(111) (adapted from[START_REF] Varykhalov | Effect of noble-metal contacts on doping and band gap of graphene[END_REF]) and d) Gr/Ag[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] (adapted from[START_REF] Varykhalov | Effect of noble-metal contacts on doping and band gap of graphene[END_REF]).

Figure 2 . 5 :

 25 Figure 2.5: Calculated electronic band structure around the K Gr -point with λ I =12 µeV > λ ext =6 µeV for a) C 6v and b) C 3v symmetries (adapted from [104]), where λ I and λ ext represent the strength of intrinsic and extrinsic SOC respectively.

Figure 2 . 6 :

 26 Figure 2.6: Spin texture due to a) Rashba and b) linear Dresselhaus SOC. c) When both are present with equal magnitude, the SO field aligns along[START_REF] Bychkov | Properties of a 2d electron gas with lifted spectral degeneracy[END_REF]. The arrows represent the SO field (adapted from[START_REF] Koo | New perspectives for Rashba spin-orbit coupling[END_REF]).

Figure 2 . 7 :

 27 Figure 2.7: a) Dispersion of the spin-orbit split surface states on bare Ir(111) (adapted from[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]). b) ARPES measurement of Au(111) (adapted from[START_REF] Hoesch | Spin structure of the Shockley surface state on Au(111)[END_REF]). c) ARPES measurement of spin-orbit split states of BiTeI (adapted from[START_REF] Ishizaka | Giant Rashba-type spin splitting in bulk BiTeI[END_REF]).

  Bychkov-Rashba Hamiltonian leads to a constant splitting of the graphene Dirac cone in the vicinity of the K point, as depicted in fig. 2.8. If the Rashba SOC is dominant with respect to the intrinsic one, we can expect a band structure as displayed in fig. 2.8c).If both Rashba and intrinsic SOC are present with comparable values, we can expect a complex spin texture with the spin character not preserved along the same band, as illustrated in fig.2.9. Such a complex behavior requires theoretical simulations in order to understand the origin of an eventual splitting of the graphene π states. Experimentally, SOC has been observed in graphene interfaced with several heavy materials. Most of them have been shown to possess bands which hybridize with the Diracb

Figure 2 . 8 :

 28 Figure 2.8: a) Pristine graphene: spin-up and spin-down states are degenerate. b)When only Bychkov-Rashba SOC is present, the spin-up and spin-down states are mixed around the band crossing points (adapted from[START_REF] Qiao | Quantum anomalous Hall effect in graphene from Rashba and exchange effects[END_REF]). c) Calculated band structure around the K Gr point with λ I =12 µeV < λ R =24 µeV (adapted from[START_REF] Kochan | Model spin-orbit coupling Hamiltonians for graphene systems[END_REF]).

Figure 2 . 9 :

 29 Figure 2.9: Calculated SOC parameters of Gr/Cu(111) as a function of Gr-Cu distance for a) Rashba SOC and b) intrinsic SOC. Calculated band structure of Gr/Cu(111) with previous SOC parameters taken at c) 2.2 Å and d) 2.5 Å (adapted from [105]). The spins s z expectation values are encoded by the colorscale, where red denotes spin-z of 1/2 and blue spin-z of -1/2.

  of such a high-Z material. Recently, giant Rashba splitting around 100 meV has indeed been observed by intercalating one monolayer of Au (Z Au =79) between Gr and Ni(111) [29]. Although a flat Au layer induces only a 10 meV spin-orbit splitting, it has been shown that a more diluted phase where Au adatoms reside in hollow-site positions (closer to graphene) provides a large enhancement of the spin-orbit splitting upto 50 -100 meV. Often both mechanisms are at play, therefore, addressing the exact origin of the spin-splitting is quite challenging. The importance of both high atomic number and hybridization between π-state of Gr and d-states of the underlying metal were also studied by respectively comparing Au intercalation with Cu intercalation (Z Cu = 29 significantly lower) and Bi intercalation (Z Bi = 83, without d electrons in the valence band) [123]. Only Au-intercalated Gr displays a spin-orbit splitting of the π-band of graphene, proving the necessity of both high atomic number and d-states in the valence band of the intercalated metal in order to induce such a "giant" SOC. A similar SOC of 100 meV has been found after intercalation of 1 ML of Au on Gr/SiC(0001) [124]. However, this SOC is much more limited in energy and momentum space. Gr on SiC forms indeed two phases with two different doping (n-and p-doped). The 100 meV SOC is visible in the p-doped phase

Figure 2 . 10 :

 210 Figure 2.10: SARPES spectra of a) Gr/Au/Ni(111) (adapted from [123]) and of b)the p-type Gr/Au/SiC(0001) in the hybridization region (adapted from[START_REF] Marchenko | Rashba splitting of 100 meV in Au-intercalated graphene on SiC[END_REF]).

Figure 2 . 11 :

 211 Figure 2.11: Fermi contours and spin texture (left), and the band structure along k x (middle) and k y (right) for a) out-of-plane (OOP) and b) in-plane (IP) exchange field. The direction of the exchange field is indicated by large yellow arrows. Small arrows give the spin projections. The used parameters are E F = 100 meV, λ I = 0 meV, λ BR = 10 meV and λ ex = 25 meV (adapted from [125]).

Figure 2 . 12 :

 212 Figure 2.12: STM evidence of the sublattice symmetry breaking of graphene on a) Ni(111) and b) Co(0001) (adapted from [45]). Tunneling parameters: V = 2 mV and I = 25 nA.

Figure 2 . 13 :

 213 Figure 2.13: Second derivative of the electronic dispersion with respect to the energy of graphene on Ni(111) measured by ARPES along the ΓK direction a) before and b)after the intercalation of one monolayer of gold (adapted from[START_REF] Varykhalov | Electronic and Magnetic Properties of Quasifreestanding Graphene on Ni[END_REF]). c) Overall band structure of graphene on Co(0001) measured along the ΓM and the ΓK directions (adapted from[START_REF] Trauzettel | Intact Dirac Cones at Broken Sublattice Symmetry: Photoemission Study of Graphene on Ni and Co[END_REF]). d) Band structure of Gr/Au(1ML)/Co(0001) measured along the ΓK direction (adapted from[START_REF] Rybkin | Magneto-Spin-Orbit Graphene: Interplay between Exchange and Spin-Orbit Couplings[END_REF]).

  represent a promising route. The intercalated layer reduces the hybridization between graphene and the ferromagnet and, therefore, reduces the shift of the Dirac point at higher binding energy. It has been shown that the intercalation of one monolayer of gold restores the Dirac cone completely (fig. 2.13). ARPES measurements of non-intercalated and intercalated Gr/FM interfaces are shown in fig. 2.13. On both substrates, the intercalation of one monolayer of gold closes the gap of 2.8 eV and brings back the Dirac cone at the Fermi level.

  to the lattice mismatch between graphene and the underlying metal surface. Several examples of moiré of graphene on different substrates measured by STM extracted from literature are depicted in fig. 2.14. Moreover different rotational domains can grow on the same substrate and cause different moiré patterns as shown in fig. 2.14c),d).

Figure 2 .

 2 Figure 2.15: a) LEED pattern of a partially graphene covered Ir(111) surface taken at 80.4 eV (adapted from [148]). b) and c) are respectively LEED patterns of the 0 • domain (R0) and the 30 • domain (R30) of Gr/Ir(111) (adapted from [149]). Unit cells of the reciprocal Ir(111) lattice (green), honeycomb carbon (dashed yellow-red) and approximate coincidence lattice (blue) are shown. d) is a LEED pattern (70 eV) of Gr/Ir(111) grown at 900 • C with several different rotational domains. e) is a LEED pattern (70 eV) of Gr/Ir(111) grown at 1100 • C.

Figure 2 .

 2 Figure 2.16: a) STM topograph of intercalated-Co domain on Gr/Ir(111) taken at (-0.7V, 1nA) (adapted from[START_REF] Decker | Atomic-scale magnetism of cobalt-intercalated graphene[END_REF]). The schematic representation and the topographic profile are represented below. b) STM topograph of Ni-intercalated region on Gr/Ir(111) taken at (0.65V, 1.21nA) (adapted from[START_REF] Pacilé | Artificially lattice-mismatched graphene/metal interface: Graphene/Ni/Ir(111)[END_REF]). The inset shows the LEED pattern of the sample. Regions A and C stand for Gr/Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF], B for Gr/Ni/Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. c) STM topograph of intercalated-Fe domain on Gr/Ir(111) (adapted from[START_REF] Bazarnik | Multi-layer and multicomponent intercalation at the graphene/Ir(111) interface[END_REF]).

  Fig.3.1 outlines the basic operation principle of an STM. The lateral position, x and y, as well as the vertical separation z between the tip and the sample surface are controlled with picometer precision by voltage signal applied to piezoelectric transducers. Once the tip and the sample are brought in thermodynamic equilibrium, their Fermi levels equalize. The bias voltage V applied to the sample rigidly shift its energy level by |eV | upward or downward depending on the voltage polarity. The tunneling current is so established from the negative electrode. Most of the tunneling current arises from the highest energy levels of the negative electrode since these levels have a longer decay into the vacuum region separating tip and sample. Thus, the tunneling current I depends exponentially on the surface-tip atoms distance and the individual surface atoms give rise to current variation as the tip scans. For topography measurements the STM is operated in the "constant current" mode. In this mode I is set to I 0 , which typical values are in between 0.5 to 5 nA. The current variation produced by the atoms of the surface are compared to I 0 in a feed-back loop and converted into a correction voltage applied to the tip z transducer. In this way I is kept constant by approaching or withdrawing the tip. The feed-back signal is recorded as a function of the (x, y) position giving a 3D map of the surface. More correctly, as it will be explained later, the signal represents the LDOS of the sample, therefore the STM maps has to be carefully interpreted in terms of atomic position.A proper quantum mechanical modeling of the process is challenging. It would require the knowledge of the electron potential in the vacuum region, the accurate description of the tip and sample electronic states and their decay into the vacuum[START_REF] Besenbacher | Scanning tunnelling microscopy studies of metal surfaces[END_REF]. There are several theories based on different approximations for those parameters. Most of them are based on the "perturbative-transfer Hamiltonian" formalism introduced by

Figure 3 . 1 :

 31 Figure 3.1: Schematic illustration of the basic principles of Scanning Tunneling Microscope (STM). The voltages applied to piezoelectric materials allow for a fine horizontal and vertical positioning of a metallic tip relative to a conductive surface. If the tip is brought close enough to the biased sample (potential V) a tunneling current I is measured.

Figure 3 . 2 :

 32 Figure 3.2: a) Schematic representation of the different energies at play in the photoemission process and its measurement. b) Scheme of the hemispherical analyzer, allowing us to differentiate the photoelectrons with respect to their kinetic energy and their angle.

25 )

 25 Let's remind us that in a crystal, k is defined modulo a lattice reciprocal space vector.It can lead to the emission of photoelectrons at different angles and with different intensities. By only considering the first Brillouin zone ( -→ G = 0), we can deduce from the

Figure 3 . 3 :

 33 Figure 3.3: Universal curve of inelastic mean free path of electrons in a solid as a function of kinetic energy. The data points shown are accumulated from many studies of different materials. The red and blue lines correspond to the given value in the text.This figure was adapted from[START_REF] Seah | Quantitative Electron Spectroscopy of Surfaces: A standard data base for electron inelastic mean free paths in solids[END_REF].

  atomic planes. Most of ARPES measurements are time-consuming (several hours-long experiments) in order to probe an entire region of the Brillouin zone, therefore the sample surface has to stay clean for the duration of the experiment. A "clean" surface means that the number of adsorbed particles stays much lower than one monolayer. In our case, every ARPES measurements have been done at a pressure below 3.10 -10 mbars, low enough to keep the sample clean.

Figure 3 . 4 :

 34 Figure 3.4: Photograph of the ARPES experimental set-up. The different parts are highlighted in different colours.

  is light and can prevent too much damages of the chamber by the ionic plasma. The two most intense and commonly used rays of helium are the HeI and the HeII, corresponding respectively to photons with energy 21.22 eV and 40.81 eV. The photon production is done by Electron Cyclotron Resonance (ERC) induced by microwaves, creating a plasma of ionized He atoms. These excited atoms then desexcite by emitting a photon. After the cavity chamber, the UV beam goes through a monochromator constituted by a combination of a grating and a mirror which also plays the role of polarizer and is then guided to the sample in a capillary. The size of the light spot on the sample is of the order of one millimeter. All the light source set-up is motorized and can be rotated around the capillary axis, allowing to change the light polarization. The emitted photons are 90% polarized either with s-or p-polarization.

  The linear axis allow us to place the sample at the focal point of the analyzer. Moreover, once the alignment procedure is done between the lamp, the sample and the analyzer, three fixed cameras enable us to find this position quickly for the next measurements, representing a huge gain of time. Thanks to the three rotations of the sample (see fig. 3.5a)), we can explore a large region in the reciprocal space. In a first approximation, ψ induces a rotation around the Γ point in the reciprocal space, φ induces a translation in the direction along the probed region and θ induces a translation perpendicular to the probed region (see fig. 3.5b)).In this work, we do ARPES measurements mostly around the graphene K point in the BZ. In the reciprocal space, we define k x axis as the ΓK axis and k y as the perpendicular ΓM axis (fig.3.5b)). For each experiment, we set θ = φ = 0 so that the Γ point is in the center of the probed region. Our measurements are θ-scans experiments: series of scans regularly spaced by a ∆θ, at fixed φ and ψ. ψ is set so that the central pixel is on the ΓK direction. In these conditions, ∆θ corresponds to a displacement of the central pixel along the ΓK direction. The total measured area in the BZ is so only determined by the chosen θ range (fig.3.9c)). For each scan, we compensate x, y and z to keep the sample at the focal position.The goniometer is placed in a flux cryostat which is filled either with liquid helium or liquid nitrogen. A temperature sensor (Cernox resistor) placed near the sample plate is measuring the sample temperature but it can also be estimated by fitting the Fermi edge of an ARPES image. For liquid helium, we measure a temperature of 10 K by the temperature sensor, 40 K for a glued gold foil on the sample plate and 50 K for an unprepared Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] substrate by fitting the Fermi edge. All the measurements for samples with graphene are done with liquid helium, but some samples without graphene are measured with liquid nitrogen.

Figure 3 . 5 :

 35 Figure 3.5: a) Schematic representation of the three rotation angles of the sample with respect to the incidence plane of the analyzer. b) Schematic representation of the effect of these angles on the displacement of the probed region in the reciprocal space (first Brillouin zone only).

Figure 3 . 6 :Figure 3 . 7 :

 3637 Figure 3.6: a) Schematic representation of the BZs of Gr and Ir with marked highsymmetry points. The proportion are respected. b) Zoom in the vicinity of both K Gr and K Ir points. The four directions of ARPES images are shown by colored full lines.The scale is respected for the BZs but not for the ARPES directions.

  fig. 3.6b).

  3 eV. 1-dimensional curves either at one specific a) EDCs b) MDCs

Figure 3 . 8 :Figure 3 . 9 :

 3839 Figure 3.8: ARPES measurements of Ir(111) along the pΓK Ir direction represented by a) EDCs and b) MDCs. The EDCs are taken every 0.02 Å -1 and the MDCs every 30 meV.

Fig. 3 .

 3 Fig.3.9 reports the electronic dispersion of the Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] surface measured using the two sets of parameters described above, along with the corresponding measured areas in the reciprocal space at the Fermi level (fig.3.9c)). We observe that the intensity is different for a same band between fig.3.9a) and fig.3.9b) i.e. for two different incident photon energies. Such apparent difference is caused by matrix element effects as discussed previously. Therefore, in the following, data can appear "different" for different experimental configurations.

  • C in order to immediately promote intercalation without forming Co clusters on graphene, which could be responsible of the low quality of the measured electronic energy dispersion. Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] substrate has been cleaned in UHV environment (base pressure < 3.10 -10 mbars) by cycles of Ar + sputtering at 1 keV and further annealing at 1400 K under oxygen pressure of 2.10 -8 mbars. The complete graphene layer has been grown by CVD at 1100 • C under an ethylene pressure of 5.10 -8 mbars for 30 minutes. Deposition of Co has been done by molecular beam epitaxy (MBE), meaning by evaporating a solid elemental rod at a very low flux (< 1Å/min), on the sample heated at 400 • C. After evaporation, the sample has been further annealed at 400 • C for 30 minutes to let Co diffuse on the surface and intercalate, as previously discussed. An increase of the moiré corrugation with respect to the non-intercalated graphene is expected due to a stronger interaction between graphene and Co with respect to graphene and Ir[START_REF] Decker | Atomic-scale magnetism of cobalt-intercalated graphene[END_REF].

Figure 4 . 1 :

 41 Figure 4.1: a) 50x50 nm 2 image taken at (-1V, 1nA) of 0.5 ML of Co deposited on Gr/Ir(111) at 400 • C. Colored lines with numbers stand for the profiles shown in b). b) Apparent height profiles.

Fig. 4 .

 4 Fig. 4.1a) presents a 50x50 nm 2 STM image of the sample after the deposition of 0.5 ML of Co. Both Gr/Ir and Gr/Co/Ir moiré patterns are visible and the intercalated domains can clearly be distinguished by their higher corrugation. We measured a corrugation of 10±5 pm for Gr/Ir(111) moiré pattern and 95±30 pm for the intercalated Co (fig. 4.1b)).

Fig. 4 .

 4 Fig. 4.2 shows STM images of the same sample at larger scale, where graphene is covering almost all the substrate surface. However, an extremely low amount of Co is intercalated under graphene, and only at the Ir substrate step edges. The rest of the

Figure 4 . 2 :

 42 Figure 4.2: a) and b) are 150x150 nm 2 images of Gr/Co(0.5ML)/Ir(111) taken at (-1V, 1nA). Left: raw topographic images. Right: same topographic images with bare Ir(111) colored in blue, intercalated Co in red, grain boundaries of graphene in black.A white circle is highlighting a 3D Co cluster.

4 . 3

 43 and 4.4). It appears that the width of the intercalated regions along the substrate atomic steps is increasing and the total intercalated surface rises from 3% to 7%. However the appearance of the moiré pattern, which has been measured for several scanning parameters, is dramatically changing. The two moiré patterns of intercalated regions for both 400 • C and 500 • C are depicted in fig. 4.4. Line profiles in fig. 4.4c) do not present any difference, neither

Figure 4 . 3 :Figure 4 . 4 :

 4344 Figure 4.3: a) 150x150 nm 2 and b) 100x80 nm 2 images of the 500 • C sample taken at (-1V, 1nA). Left: raw topographic images. Right: same topographic images with bare Ir(111) colored in blue and intercalated Co in red. White circles are highlighting 3D Co clusters on top of graphene or Ir(111).

  been grown by TPG. The average size and density of the graphene flakes are determined by the flashing temperature and their duration[START_REF] Poelsema | Growth of graphene on Ir(111)[END_REF]. In our work, one TPG cycle was constituted by a flash at 1150 • C for 20 s after exposing the sample surface to an ethylene pressure of 2.10 -7 mbars for 5 min at room temperature. The total graphene surface coverage is then controlled by the number of TPG cycles. STM measurements have been realized on two different iridium crystals, referred as Crystal 1 and Crystal 2 in the following. The cleaning parameters of Ir substrates were the same as reported in the previous section. Successive TPG cycles were realized on both crystals and the corresponding topographic measurements are displayed in fig. 4.5 (for example TPG2 corresponds to two cycles of TPG).

Figure 4 . 5 :

 45 Figure 4.5: 200x200 nm 2 topographic images of a) TPG1 (-1V, 1nA) and b) TPG2 (-1V, 1nA) on Crystal 1, c) TPG1 (1V, 500pA), d) TPG2 (0.2V, 100pA) and e) TPG3 (0.2V, 100pA) on Crystal 2. Left: raw topographic measurements. Right: same topographic images with graphene flakes colored in blue and iridium atomic steps in black.

Figure 4 . 6 :

 46 Figure 4.6: a), b) 200x1600 nm 2 images of two different regions of TPG3 on Crystal 2 taken at (0.1V, 500pA). a) is referred as region A while b) is referred as region B. Top: raw topographic images. Bottom: same topographic images with graphene flakes colored in blue and iridium atomic steps in white.

Figure 4 . 7 :

 47 Figure 4.7: a) shows the AES C peak for TPG cycles from 1 to 7. b) Evolution of surface coverage measured both by AES and STM with respect to the TPG cycles number.

Figure 4 . 8 :

 48 Figure 4.8: LEED patterns taken at 70 eV of a) TPG1, b) TPG2, c) TPG3, d) Ir(111) and e) a complete graphene layer. On d) and e), blue and red circles mark the Ir and Gr spots respectively.

Figure 4 . 9 :Fig. 4 .

 494 Figure 4.9: 20x20 nm 2 images of a) Gr/Ir, b) Gr/Pd/Ir and c) Gr/Co/Ir. d) Topographic profiles for the moiré at play: Gr/Ir (black), Gr/Pd/Ir (blue) and Gr/Co/Ir (red).

Figure 4 .

 4 Figure 4.10: a) 400x400 nm 2 and b) 200x200 nm 2 STM images of 0.1ML Co -50% Gr taken at (-1V, 1nA). Left: raw topographic images. Right: same images with intercalated Co regions colored in red and the substrate atomic steps in white. The inset on the left in a) is a 100x100 nm 2 zoom of the region marked by a red square.

Figure 4 . 11 :

 411 Figure 4.11: 200x200 nm 2 STM images of 0.3 ML Pd -50% Gr taken at a) (-1V, 1nA) and b) (0.2V, 100pA). Left: zoom of the 50x50 nm 2 region marked by a red square. Center: raw topographic images. Right: same images with intercalated Pd regions colored in red, non-intercalated Pd in yellow and the substrate atomic steps in white.

Figure 4 .

 4 Figure 4.12: a), b) 500x500 nm 2 STM images (-1V, 1nA) of two regions of 0.5ML Co -50% Gr. Left: zoom of the 100x100 nm 2 region marked by a red square. Center: raw topographic images. Right: same images with intercalated Co domains colored in red, non-intercalated graphene in blue and substrate atomic steps in white.

  amount of intercalated Pd as a function of the deposited Pd quantity. Topographic images for Pd deposition of 0.2 ML and 0.5 ML are shown in fig. 4.13 and fig. 4.14, for two different regions of the sample. For the 0.2 ML, region 1 (fig.4.13a)) shows only intercalated Pd while region 2 (fig.4.13b)) shows both Pd/Ir islands and intercalated Pd.

Figure 4 . 13 :

 413 Figure 4.13: 200x200 nm 2 STM images of 0.2 ML of Pd on a 65% Gr (0.1V, 500pA) for two regions called a) region 1 and b) region 2. Left: zoom of the 70x70 nm 2 region marked by a red square. Center: raw topographic images. Right: same images with intercalated Pd regions colored in red, non-intercalated Pd in orange and substrate atomic steps in white.

Figure 4 . 14 :

 414 Figure 4.14: 200x200 nm 2 STM images of 0.5 ML of Pd on a 65% Gr (0.1V, 500pA) for two regions called a) region 1 and b) region 2. Left: zoom of the 70x70 nm 2 region marked by a red square. Center: raw topographic images. Right: same images with intercalated Pd regions colored in red, non-intercalated Pd in orange and substrate atomic steps in white.

Figure 4 . 15 :

 415 Figure 4.15: 200x200 nm 2 STM images of 0.9 ML of Pd on a 65% Gr (0.1V, 500pA) for two regions called a) region 1 and b) region 2. Left: zoom of the 70x70 nm 2 region marked by a red square. Center: raw topographic images. Right: same images with intercalated Pd regions colored in red, non-intercalated Pd in orange and substrate atomic steps in white.

Fig. 4 .

 4 Fig. 4.16 displays ARPES measurements along the M Gr K Gr Γ direction up to -1.5 eV below the Fermi level for TPG2, TPG3 and a complete graphene layer (grown by CVD at 1100 • C). The measured surface coverages by AES are 70% for TPG2, 85% for TPG3 and 100% for the complete graphene layer. These measurements have been done with an incident photon energy of 21.22 eV (HeI), a s-polarization and at 50 K (liquid helium). The electronic energy dispersion looks very similar in the three cases (fig. 4.16a),b),c)) with the Dirac cone easily identifiable. A very intense state is located near the Fermi level at the K Gr point (it originates from the Ir(111) substrate as discussed in the next chapter) and prevents us to precisely determine the doping of the Dirac cone.

Fig. 4 .

 4 Fig. 4.16d) displays MDCs taken at -0.4 eV for the three samples along the directions shown by the green dashed line in 4.16a). The bandwidth (often called Γ) is indeed proportional to the inverse of the quasiparticle lifetime τ [172, 173, 174, 175, 176]. The contributions of the lifetime broadening are mainly originating from electron-electron, electron-phonon and electron-defect scattering. At this energy, the MDC intercepts two branches of the Dirac cone along both M Gr K Gr and K Gr Γ directions. An usual

Figure 4 . 16 :

 416 Figure 4.16: ARPES measurement taken along the M Gr K Gr Γ direction of a) a full graphene monolayer, b) TPG2 and c) TPG3. d) MDCs taken at -0.4 eV of the three samples (depicted by the green dashed line in a)). The values of the half width at half maximum are displayed for both M Gr K Gr and K Gr Γ directions.

  up to -3.8 eV below the Fermi level. These measurements have been done with an incident photon energy of 40.81 eV (HeII) and a s-polarization, at 50 K (liquid helium). A quick observation reveals a very intense Dirac cone reaching the Fermi level for both samples. Three "minigaps" (originating from the moiré superpotential)[178,[START_REF] Kralj | Graphene on Ir (111) characterized by angle-resolved photoemission[END_REF] are visible on both cones, marked by black circles in fig.4.17b), even though the corresponding replicas are not measured. The Ir state appears more intense for TPG3 than for the complete Gr layer with respect to the Dirac cone.

Fig. 4 .

 4 Fig. 4.17 shows two MDCs taken at -0.4 eV (fig. 4.17c)) and -1.5 eV (fig. 4.17d)) of the two samples. At -0.4 eV, only the HWHM is measurable for both branches of the Dirac cone (along M Gr K Gr and K Gr Γ directions) and it is 1.5 times larger for the TPG3 sample than for the complete Gr. Moreover, the intensity of the Dirac cone with respect to the one of the Ir state is increasing by a factor of 2.5 when the graphene

1 -Figure 4 . 17 :

 1417 Figure 4.17: ARPES measurement taken along the M Gr K Gr Γ direction of a) a complete Gr layer and b) TPG3. "Minigaps" are marked by black circles in b). The green and orange dashed lines in a) correspond to the profile directions of the MDCs (c),d))and EDCs (e),f)). MDCs taken at c) -0.4 eV and d) -1.5 eV. EDCs taken on e) the M Gr K Gr and f) the K Gr Γ directions.

A

  short overview of the previous published scientific papers on Gr/Co systems is presented in fig. 5.1. The first image (fig. 5.1a)) shows the measurement of Gr/Co(1ML)/Ir(111) taken along the ΓK Gr direction [61]. The π band of graphene reaches K Gr around -3 eV and Co d state is visible at about -1.5 eV. Figure 5.1b) shows ARPES measurements of Gr/Co(2ML)/Ir(111) taken along ΓM K Gr Γ directions [28]. The π band of graphene reaches the K Gr point at -2.5 eV and Co 3d bands are identified at -1.6 eV and near the Fermi level. The last image (fig. 5.1c)) shows the ARPES measurement of Gr/Co(0001) taken along the M ΓK directions [45]. The π band of graphene reaches the K point around -3 eV. These experiments demonstrate that the presence of Co under graphene shifts the π band of about -2.5, -3 eV below the Fermi level and Co 3d states are present at the K point around -1.6 eV. These features are common to the intercalated Co layers and to graphene lying on bulk Co. b) Gr/Co(2ML)/Ir c) Gr/Co(0001)

Figure 5 . 1 :

 51 Figure 5.1: ARPES measurements a) of Gr/Co(1ML)/Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] taken at a photon energy of 63 eV along the ΓK direction (adapted from[START_REF] Pacilé | Electronic structure of graphene/Co interfaces[END_REF]), b) of Gr/Co(2ML)/Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] taken at a photon energy of 94 eV along the ΓM KΓ directions (adapted from[START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF]) and c) of Gr/Co(0001) taken at a photon energy of 62 eV (adapted from[START_REF] Trauzettel | Intact Dirac Cones at Broken Sublattice Symmetry: Photoemission Study of Graphene on Ni and Co[END_REF]).

Figure 5 . 2 :

 52 Figure 5.2: a) Schematic representation of the BZs of Gr and Ir with marked highsymmetry points. The proportion are respected. b) Zoom in the vicinity of both K Gr and K Ir points. The four directions of ARPES images are shown by colored full lines.The scale is respected for the BZs but not for the ARPES directions.

Figure 5 . 3 :

 53 Figure 5.3: ARPES measurements taken along the M Ir K Ir Γ direction of a) Ir(111), b) Gr/Ir(111) and c) Co/Ir(111). The gray dashed lines are highlighting the bands to guide the eyes. The red dashed line in b) stands for the 3NN-TB fit. d) DFT-calculated band structure of Ir(111), adapted from[START_REF] Pletikosić | Photoemission and density functional theory study of Ir(111); Energy band gap mapping[END_REF]. The orange rectangle shows our ARPES measurement region. e) Identified bands for the three samples along with the 3NN-TB fit. f) EDC of the three samples taken at K Ir .

Fig. 5 .

 5 3a),b),c) displays the electronic dispersion along the M Ir K Ir Γ direction for the three samples. All bands are highlighted by dashed gray lines to guide the eyes. A more accurate determination of the bands has been done by fitting a Gaussian peak with a linear background either on EDC or MDC (see fig. 5.3e)). The Ir(111) sample presents a gaped region (from below the Fermi level to -1 eV) and three surface states are easily visible, indicated as S 1 , S 2 and S 3 [62] (see fig. 5.3a)). Their energy at K Ir point can be determined on the EDC (fig. 5.3f)), finding -1.05 and -1.32 eV for S 2 and S 3 respectively, while the S 1state is located at the Fermi level. The S 2 and S 3 states remain nearly flat along the K Ir Γ direction but disperse to higher energy along the M Ir K Ir direction. Our ARPES measurements are in agreement with DFT-calculated band structure (fig.5.3d)). A very intense low-dispersing state is also present mostly along the K Ir Γ direction and it reaches -1.70 eV at K Ir (indicated as I in the simulations presented in[START_REF] Pletikosić | Photoemission and density functional theory study of Ir(111); Energy band gap mapping[END_REF]). Between -2 and -3.5 eV, DFT predicts an other band gap with four states crossing the K Ir point.Our ARPES measurement only shows two states in this region and an other state is present around -4 eV.The Gr/Ir(111) ARPES measurement (fig.5.3b)) shows a very intense Dirac cone that is well described by its 3NN-TB fit (red dashed line). Besides the cone, the S 2 state of Ir is still visible on both directions along with the I state on K Ir Γ direction. The S 3 state is hidden by the Dirac cone and no other state are detected below -2 eV.

Fig. 5 .Figure 5 . 4 :

 554 Figure 5.4: ARPES measurements taken along the M K Gr Γ directions for a) bare Ir(111), b) Gr/Ir(111) and c) Co/Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. The vertical dashed black lines stand for the K Gr point while the white one is for the K Ir point. d) Identified bands for the three samples taken along the M K Gr Γ direction. e) displays the EDC taken at the K Gr point. Horizontal coloured lines represent the baseline for each EDC, the vertical dashed black line stands for the Fermi level.

Figure 5 . 5 :

 55 Figure 5.5: ARPES measurements taken along the M Gr K Gr Γ direction for a) Co/Ir(111), b) Gr/Co/Ir-400 • C and c)Gr/Co/Ir-650 • C. d) Schematic representation of the identified bands of the three samples. e) EDCs taken at K Gr .

Figure 5 . 6 :

 56 Figure 5.6: 50x50 nm 2 topographic images of intercalated Co at a) 400 • C and b) 500 • C. The white circles and ellipses show small areas of intercalated Co.

Fig. 5 .

 5 Fig. 5.7a),b),c) shows LEED patterns for the different growth steps of the Gr/Co/Ir-650 • C sample: a) a complete graphene layer grown by CVD at 1100 • C, b) after the deposition of a ML of Co at room temperature and c) after the annealing procedure at 650 • C. They are compared with the LEED of Gr/Co/Ir-400 • C (fig. 5.7d)) and the ones

Figure 5 . 7 :

 57 Figure 5.7: LEED patterns taken at 70 eV of a) a complete graphene layer grown by CVD at 1100 • C, b) with a ML of Co deposited at room temperature, c) after an annealing at 650 • C and d) 1 ML of Co intercalated at 400 • C under a 70% surface graphene. LEED patterns of a complete graphene layer e) before and f) after the deposition and intercalation of 2 ML of Co at 600 • C (adapted from [28]).

1 ÅFigure 5 . 8 : 1 ÅFigure 5 . 9 :

 158159 Figure 5.8: ARPES images of Gr/Co<1ML/Ir taken along a) the M Gr K Gr Γ, b) the pΓK Gr , c) the M Ir K Ir Γ and d) the pΓK Ir directions. The vertical dashed lines correspond to K Gr (black) and K Ir (white). The red dashed lines stand for 3NN-TB fit of a complete graphene layer. Constant energy maps taken at -0.7 eV of e) Gr/Co<1ML/Ir and f) Gr/Ir. The black (white) dot represents K Gr (K Ir ). The red lines stand for 3NN-TB fit of a complete graphene layer.

Figure 5 . 10 :

 510 Figure 5.10: ARPES images taken along the M Gr K Gr Γ direction of a) Gr/Ir, b) Gr/Co<1ML/Ir-400 • C and c) Gr/Co<1ML/Ir-650 • C. The linear fits are plotted in the energy range from -0.8 to -0.4 eV in a) blue, b) red and c) black. The red dashed lin in a) corresponds to the 3NN-TB fit. The red dashed lines in c) stand for the linear fit of Gr/Co<1ML/Ir-400 • C. d), e) and f) are zoom of a), b) and c) in the energy range from -1 to 0.05 eV in the vicinity of K Gr . The horizontal error bars correspond to the band widths found by the Gaussian fit. g) Three MDCs of Gr/Ir(111) (black dashed lines) with the double Gaussian fit (green) and its two components (red and blue). h) Same as g) for Gr/Co<1ML/Ir-400 • C. i) MDCs of Gr/Co<1ML/Ir-650 • C. The red dots correspond to the peak positions, displayed in f).

Figure 5 . 11 :

 511 Figure 5.11: Constant energy maps of Gr/Co<1ML/Ir-400 • C taken at a) -1.5 eV, b) -1.7 eV and c) -1.9 eV. Constant energy maps of Gr/Co<1ML/Ir-650 • C taken at d) -1.5 eV, e) -1.7 eV and f) -1.9 eV. The 3NN-TB is shown by the red lines. On d), e) and f), the gray dashed lines are guide for the eyes for the Dirac cone. The black lines in a) are the directions for the profiles displayed in figure 5.12.

Figure 5 . 12 :

 512 Figure 5.12: Constant energy map of Gr/Co<1ML/Ir-650 • C taken at a) -1.5 eV and c) -2.2 eV. The 3NN-TB are shown in red and blue lines. Their energies correspond to red and blue dashed lines in b). b) The dots are experimental positions of the Dirac cone found on profiles taken along the black lines shown in figure 5.11a) for the 400 • C-annealed sample (black) and the 650 • C-annealed sample (blue). The full lines correspond to the previous linear fits near the Fermi level.

  • C (above the Ir-Co intermixing temperature of 500 • C[START_REF] Drnec | Surface alloying upon Co intercalation between graphene and Ir(111)[END_REF]), no change in the band structure is observed, excepted a decrease of the ARPES measurement quality, which reflects a degradation of the crystalline quality of the sample. This structural degradation is confirmed by topographic (STM) and diffraction (LEED) measurements. It is probably caused by the formation of a disordered Co-Ir surface alloy starting at 500 • C, extending over a thickness of about 2-3 ML[START_REF] Drnec | Surface alloying upon Co intercalation between graphene and Ir(111)[END_REF].To address the effect of the Co-Ir alloy on the Dirac cone, we studied Co intercalation in the submonolayer regime. Upon deposition and intercalation at 400 • C of 0.6 ML of Co, both Co states, GrCo state and the pristine Dirac cone are observed, ensuring the presence of unintercalated graphene. The Co-derived states are more intense than the Dirac cone, confirming that most of the sample is covered by Co. A further annealing at 650 • C changes dramatically the band structure of the sample. The Dirac cone is still present but changes compared to pristine graphene. In the energy range close to the Fermi level, the electrons velocity (slope of the E( k) dispersion) is increasing by a factor of about 2. Further investigations at lower energies confirm that the energy difference between the measured cones is momentum dependent and different along the two high-symmetry directions. None of these effects were observed for an intercalated ML of Co, suggesting that this Dirac cone modification is related to the intercalated Co quantity. The Co-Ir surface alloy forming at 650 • C can indeed have different structures depending on the deposited Co amount and in our case, we speculate that graphene is lying on a Ir-rich alloy, thus preserving partially its electronic dispersion. The difference of the growth methods can also be at the origin of such a change in the alloy composition. If Co is firstly deposited at RT and then annealed to intercalate, the 3D growth of Co clusters at RT could lead to different intercalation and alloying processes when compared to a 2D growth at 400 • C. the study of the band structure of Gr/Pd hybrid systems. We intercalated palladium under graphene to induce spin-orbit coupling in the graphene band structure. A determining parameter of the strength of the intrinsic SOC of a material is its atomic number. Therefore, inducing SOC in graphene band structure presents a real challenge, due to its low atomic number (Z C = 6). As discussed in section 2.2.2, induced spin-orbit effects can either have an intrinsic or extrinsic (called Rashba) origin. So far, the hybridization of heavy materials (Z Au = 79, Z P t = 78, Z Ir = 77) with graphene has been proven to induce an intrinsic SOC in graphene, reaching a maximal SO splitting of 100 meV for a ML of gold intercalated between Gr and Ni[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] [START_REF] Marchenko | Graphene for spintronics: giant Rashba splitting due to hybridization with Au[END_REF].These heavy materials have a weak interaction with graphene[START_REF] Vanin | Graphene on metals: A Van Der Waals density functional study[END_REF] (31 meV/C-atom for C-Au, 33 meV/C-atom for C-Pt), with inter-atomic distances superior than 3 Å [31] (d C-Au = 3.168 Å, d C-Ir = 3.392 Å).

Figure 6 . 1 :Figure 6 . 2 :

 6162 Figure 6.1: a) LEED patterns of three rotational domains (R2• , R5 • and R10 • ) of Gr/Pd grown by segregation (adapted from[START_REF] Murata | Orientation-dependent work function of graphene on Pd (111)[END_REF]). Dashed and solid lines show Pd and Gr spots. b) LEED pattern of a single-oriented graphene layer grown by segregation on an amourphous Pd silicide film (adapted from[START_REF] Kim | Millimeter-Scale Growth of Single-Oriented Graphene on a Palladium Silicide Amorphous Film[END_REF]). No moiré is visible, confirming the amorphicity of the underneath film. The red hexagon marks the R30 • directions, no spots are visible.

Figure 6 . 3 :

 63 Figure 6.3: STM image of a) Gr/Pd/SiC(0001) (adapted from [68]) and of b)Gr/Pd/Ru(0001) (adapted from[START_REF] Huang | Intercalation of metal islands and films at the interface of epitaxially grown graphene and Ru (0001) surfaces[END_REF])

  -10 mbars) by cycles of Ar + sputtering at 1 keV and further annealing at 1400 K under oxygen pressure of 2.10 -8 mbars. The ARPES experiments have been realized with an incident photon energy of 21.22 eV (HeI) and with a p-polarization, up to an energy of -1.5 eV below the Fermi level. The Ir(111) and Pd/Ir(111) sample have been cooled down by liquid nitrogen (T > 70 K). Since the experiments conditions are different from the one of the previous chapter, the matrix element effects change the measured band structure. Therefore, we first present again the electronic dispersion of Ir(111).

Fig. 6 .

 6 Fig.6.[START_REF] Wilcoxon | Photoluminescence from nanosize gold clusters[END_REF] shows the ARPES measurement of Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] around both K Gr and K Ir points of the first Brillouin zone (fig.6.4e)). The DFT calculation of the Ir(111) band structure, adapted from[START_REF] Pletikosić | Photoemission and density functional theory study of Ir(111); Energy band gap mapping[END_REF], is also shown in fig.6.4d). As we already saw in chapter 5, the Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] substrate has conveniently a band gap in the measured area. We retrieved the three surface states, indicated as S 1 , S 2 and S 3[START_REF] Pletikosić | Photoemission and density functional theory study of Ir(111); Energy band gap mapping[END_REF]. The M Ir K Ir Γ cut shown in fig.6.4a) is remarkably consistent with DFT-calculated band structure. The S 2 and S 3 remain nearly flat along the K Ir Γ direction but disperse to higher energy along the M Ir K Ir direction. Their precise energies at the K Ir point have been determined on the EDC shown in fig.6.4c). We found -1.05 and -1.32 eV for S 2 and S 3 respectively, consistently with previous measurements. These three surface states are still present near the K Gr point and their energies are -0.91 and -1.06 eV at K Gr . The S 1 state being very close to the Fermi level, its energy is difficult to determine with precision.

Figure 6 . 4 :

 64 Figure 6.4: ARPES measurements of bare Ir(111) taken respectively along a) the M Ir K Ir Γ direction and b) the M Gr K Gr Γ direction. c) shows EDC taken at both K Gr and K Ir points. d) Ir(111) band structure calculated by DFT (adapted from[START_REF] Pletikosić | Photoemission and density functional theory study of Ir(111); Energy band gap mapping[END_REF]). e) Schematic representation of the BZ of both Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] and Gr/Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]. The right part is a zoom around the K points of the system and describes the four cuts which will be used to present ARPES data.

  The deposition has been done by MBE on the substrate heated at 400 • C. The Pd quantity has then been verified to be 1 ML by AES. With the chosen growth conditions Pd grows pseudomorphic to the Ir(111) substrate as demonstrated by the LEED diffraction pattern in fig. 6.5f) where only the six spots corresponding to the Ir(111) surface are visible. We present the ARPES measurement of this sample along both the M Ir K Ir Γ and the the M Gr K Gr Γ directions (fig. 6.5a) and b) respectively). Two quantum well states (QWSs) develop in the band gap of Ir(111) (DFT calculations demonstrate that these two states originate from the Pd vertical confinement). Those low dispersing states are situated between -0.5 and -1.0 eV in the measurement region. As expected their interaction between the Ir surface states is quite strong showing a shift of few hundreds of meV of the S 2 and S 3 states. The two Pd-QWSs have a similar dispersion with an energy separation that goes from 120 meV at the K Gr point to 170 meV at the K Ir point, as shown by the energy dispersion curves (EDC) in fig. 6.5c). In order to understand the origin of the splitting of the QWSs, fig. 6.5d),e) displays DFT calculation of the Pd/Ir(111) system. Before comparing DFT calculations with our experimental data, we report the DFT computational details. These simulations have been done by Pr. E. Voloshina and Pr. Y. Dedkov. DFT calculations based on plane-wave basis sets of 500 eV cut-off energy

Figure 6 . 5 :Fig. 6 .

 656 Figure 6.5: ARPES measurements of bare Pd/Ir(111) taken respectively along a) the M Ir K Ir Γ direction and b) the M Gr K Gr Γ direction. c) shows EDCs taken in the momentum range depicted by the red arrows in b). Pd/Ir(111) band structure calculated by DFT d) without and e) with SOC. Red and blue dots in e) correspond to majority and minority spins. The orange rectangles show the region we are measuring with ARPES. f) LEED pattern of Pd/Ir(111) taken at 70 eV.

Figure 6 . 6 :

 66 fig.6.6c). The hybridization between graphene π and Pd 4d z 2 is clearly visible at the HCP high-symmetry position of the Gr/Pd/Ir[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF] interface. Such modifications in the

Figure 6 . 7 :

 67 Figure 6.7: ARPES images taken along the M Gr K Gr Γ direction of a) Gr/Ir and b) Gr/Pd/Ir. c) EDCs of Gr/Pd/Ir at the wave vectors indicated by the white arrows in b). The dashed lines correspond to the experimental data while the green, red and blue lines correspond to the fitted function, and its two Gaussian components respectively. d) Positions of the Gaussian centers in the momentum region enclosed by the two red dashed lines in b). The error bars are given only for the three fits in c).

  6.7b), with a doubleGaussian function summed with a linear background. Examples of such fitting procedure are given in fig.6.7c) where the green curves represent the fitted functions while red and blue curves correspond to its two components. The resulting Gaussian peak positions are shown in fig.6.7d). For sake of simplicity only the error bars corresponding to the three profiles shown in fig.6.7c) are presented. For the hole-like dispersing state, two separated electronic contributions along the M Gr K Gr Γ direction have been detected, in a region of about 0.3 Å -1 centered at the K Gr point. This energy separation reaches more than 200 meV and is strongly reduced at the K Gr point. The situation of the low dispersing state is rather more complex. While in the majority of the considered reciprocal space points the two components lies within the error bars, we detected a clear 200 meV energy separation along the M Gr K Gr direction at about 0.15 Å -1 from K Gr point.

  eV) a) Gr/Ir(111) b) Pd/Ir(111) c) Gr/Pd/Ir(111)

  eV) d) Gr/Ir(111) -zoom e) Gr/Pd/Ir(111) -zoom

Figure 6 . 8 :

 68 Figure 6.8: a), b), c) Spin-resolved band structures of Gr/Ir(111), Pd/Ir(111), and Gr/Pd/Ir(111), respectively, obtained after unfolding procedure and presented around the K point of the (1 × 1) graphene-derived Brillouin zone (a), c)) and Pd/Ir(111)derived Brillouin zone (b)), respectively. The size of the point gives the information about the number of primitive cell bands crossing particular (k, E) in the unfolded procedure, i.e., the partial density of states at (k, E). d), e) Zoom of the regions marked by an orange rectangle in a) and c) respectively. These regions correspond to our experimental ARPES measurements.

  diagram of PdCo alloy

Figure 7 . 1 :

 71 Figure 7.1: a) Calculated structure of PdCo clusters. First row: 34-atoms clusters, second row: 38-atoms clusters (adapted from [70]). Co atoms are in blue, Pd in gray. b) Experimental phase diagram of PdCo alloy (adapted from [216]).

  7.2a)). The dPd-dCo hybridization causes a low energy shift of the surface Pd d-band with respect to that for Pd(111) (see fig.7.2b)), with the d-band center at -2.06 eV for P d 0.75 Co 0.25 and -1.88 eV

  Relative enthalpy of mixing (eV) E-E F (eV) DOS a) Surface structure and enthalpy of CoPd alloy b) DOS of surface Pd atoms in CoPd alloy

Figure 7 . 2 :

 72 Figure 7.2: a) Calculated structure of PdCo surface and relative enthalpies of mixing with respect to the Co atomic percentage (adapted from [226]). b) Calculated d-band density of states for surface Pd atoms in P d 0.75 Co 0.25 alloy (adapted from [224]). The positive intensities correspond to states of spin-up and the negatives to spin-down. The green line marks the d-band center (averaged for the spin up and down states).

Figure 7 . 3 :

 73 Figure 7.3: STM image of successive intercalation of Fe and Co under graphene (adapted from [72]). Intercalated Co domains are highlighted in red, intercalated fe in blue.

Figure 7 . 4 :

 74 Figure 7.4: 500x500 nm 2 STM image of 0.5 ML of Co under a 50% graphene. Left: 100x100 nm 2 zoom of the region marked by a red square in the center image. Center: raw topographic image. Right: same topographic image with intercalated Co domains colored in red, unintercalated Gr in blue and substrate step edges in white.

  a) Co 0.5 ML -Pd 0.25 ML -500x500 nm 2 b) Co 0.5 ML -Pd 0.25 ML -400x400 nm 2

Figure 7 . 5 :

 75 Figure 7.5: a) 500x500 nm 2 and b) 400x400 nm 2 STM image of 0.5 ML of Co, followed by 0.25 ML of Pd on a 50% graphene. Left: raw topographic image. Right: same topographic image with intercalated domains colored in red, unintercalated Gr in blue, metal on Ir(111) in gray and substrate step edges in white.

Figure 7 . 6 :

 76 Figure 7.6: a), b) 200x200 nm 2 STM image of 0.5 ML of Co, followed by 0.25 ML of Pd on a 50% graphene. Left: 100x100 nm 2 zoom of the region marked by a red square in the center image. Center: raw topographic image. Right: same topographic image with intercalated domains colored in orange and purple for the two different moiré, unintercalated Gr in blue, metal on Ir(111) in gray and substrate step edges in white. c) Apparent height profiles along the orange and purple lines in a), left. d) Small-scale STM topographs of Gr/Co(0001) (adapted from [45]).

Figure 7 . 7 :

 77 Figure 7.7: LEED patterns taken at 70 eV of a) a complete graphene layer, b) 1 ML of Pd intercalated under a 85% graphene, c) Gr(70%)/Pd(80%)-Co(20%)/Ir and d) Gr(70%)/Pd(70%)-Co(30%)/Ir.

Figure 7 . 8 :

 78 Figure 7.8: ARPES measurements taken along the M Gr K Gr Γ direction of a) Gr(85%)/Ir(111) with p-polarization, b) Gr(85%)/Pd/Ir(111) with p-polarization, c) Gr(85%)/Pd/Ir(111) with s-polarization, d) Gr(70%)/Pd(80%)-Co(20%)/Ir(111) with p-polarization, e) Gr(70%)/Pd(70%)-Co(30%)/Ir(111) with s-polarization. The 1NN-TB fit of Gr/Ir is shown by red dashed lines.

SAMPLEFigure A. 2 :

 2 Figure A.2: Schematic representation of the goniometer. The rotation axis for θ, φ and ψ are marked by dashed lines respectively black, green and red.

cos 2 θ( 1 -

 21 ϕ the angle shown in fig. A.1. To obtain the k components of this wave vector, we need to project it on the sample surface. Therefore, we need to calculate the sample surface unit vectors ( x S , y S ) with respect to the reference axis. Now, by replacing u φ and φ in equation A.2, we obtain the φ rotation matrix: R φ (θ, φ) = R(φ, u φ ) = cos φ) + cos φ sin θ sin φ -sin θ cos θ(1 -cos φ) -sin θ sin φ cos φ -cos θ sin φ cos θ sin θ(1 -cos φ) cos θ sin φ cos φ + (1 -cos φ) sin 2 θ

  2.1.3 to obtain:k x = 0.512 E kin (eV ) , we do mostly θ-scans experiments. For one experiment, φ and ψ are fixed and only θ is varying. The rotation matrices are therefore only depending on θ, and we obtain:R(θ) = R ψ R φ R θ (A.12a) k x (θ, ϕ) = 0.512 E kin (eV )k y (θ, ϕ) = 0.512 E kin (eV ) R(θ) the global rotation matrix constituted of the three θ, φ and ψ rotations. Lets first take the sample perfectly parallel to the incidence plane of the analyzer (θ = φ = 0 by definition). The measured region in the reciprocal space (at a constant energy) is then a line (see fig. A.3a)) with coordinates: k x = 0.512 E kin sin ϕ sin ψ (A.13a) k y = 0.512 E kin sin ϕ cos ψ (A.13b)

1 ( 1 ( 1 ( 1 (

 1111 Figure A.3: a) Probed line for θ = φ = 0 in the reciprocal space. The lines are centered on the Γ point. The ψ=0 is chosen so that the line is along the k y axis. b) Probed regions for HeI (red) at the Fermi level (solid line) and at -1.5 eV (dashed line), and for HeII (blue) at the Fermi level (solid line) and at -4.5 eV (dashed line) for the experiments described in this work.

1 ( 1 (

 11 • of angular acceptance, corresponding to a resolution of δϕ = 30 • 1040 = 0.029 • . The maximal δk for both k x and k y caused by δϕ are then:δk x = 0.512 E F sin θ max |cos 15 • -cos(15 • -δϕ)| (A.19a) δk y = 0.512 E F |sin δϕ -sin 0 • | = 0.512 E F |sin δϕ| (A.19b)The calculated values for both used experimental conditions are:δk x (HeI) = 2.10 -4 Å -1 < δk y (HeI) = 1.1.10 -3 Å -A.20a) δk x (HeII) = 2.10 -4 Å -1 < δk y (HeII) = 1.6.10 -3 Å -A.20b)It has to be noticed that the δϕ is very small compared to the chosen step for θ. The θ step is in fact determined by the analyzer entrance slit. The entrance slit is not perfectly one-dimensional but has a width w which induces a certain angular acceptance dθ of the analyzer along the x direction. The working distance between the sample and the entrance slit is fixed at d = 5.4 cm, while the slit width can be changed. We choose for our two experiments two slit widths for the two different energies used, namely w(HeI) = 0.2 mm and w(HeII) = 0.8 mm. The corresponding angle variation is then: of 0.1 • for HeI and 0.4 • fo HeII. For a fixed θ, we measure an angle range of θ ± dθ. Therefore, the maximal value of the δθ step is 2dθ so that all the angles are measured. We choose a δθ step of 0.2 • and 0.4 • for HeI and HeII respectively. These δθ steps correspond to δk x of: δk x = 0.512 E F |sin θ min -sin(θ min + δθ)| (A.22)

- 1 Figure A. 4 :

 14 Figure A.4: Constant energy map taken at -0.7 eV of Gr/Ir(111) a) before and b) after the transformation in the reciprocal space. The ΓK direction is shown in red, the M Gr K Gr directions in dashed black and the M Ir K Ir directions in dashed white.

  du graphène par croissance programmée en température (TPG) est donc étudiée. Après saturation de la surface avec des molécules d'éthylène (5 min à 2.10 -7 mbars), l'échantillon est chauffé à 1150 • C pendant 20 secondes. Ce cycle est alors répété pour augmenter la quantité de graphène. Le recouvrement de la couche de graphène est mesuré sur plusieurs images, de plusieurs régions de l'échantillon, pour une surface totale supérieure à 1 µm 2 . Des cycles successifs augmentent en effet le recouvrement du graphène. En revanche, la même croissance réalisée sur deux cristaux d'iridium différents ne permet pas d'obtenir des valeurs identiques. L'homogénéité de l'échantillon est remise en question après la mesure, sur le même échantillon, de deux régions présentant une grande différence dans le recouvrement du graphène (50% et 90%). Cette inhomogénéité 'intercalation d'une monocouche de cobalt, que ce soit sous une couche complète de graphène ou un recouvrement de 70%, ne modifie pas les états du cobalt. En revanche, le cône de Dirac n'est plus visible au niveau de Fermi. Un nouvel état (GrCo) apparait en-dessous de -3 eV, que nous ne pouvons pas identifier avec certitude avec notre résolution, mais qui a été identifié dans la littérature comme la bande π du graphène. Après un recuit de l'échantillon à 650 • C (au-dessus de la température d'alliage Co-Ir), aucun changement dans sa dispersion électronique n'est observé, à l'exception d'une baisse de la qualité des données d'ARPES, qui reflète la dégradation de la qualité cristalline de l'échantillon. Cette dégradation, confirmée par des mesures de LEED et STM, est probablement due à la formation d'un alliage de surface Co-Ir désordonné. Il serait alors couche de graphène ont été étudiées pour servir de plate-forme réactive[START_REF] Thapa | Palladium atoms and its dimers adsorbed on graphene : First-principles study[END_REF][START_REF] Cabria | Theoretical study of the transition from planar to three-dimensional structures of palladium clusters supported on graphene[END_REF]. Pour de plus larges interfaces Gr/Pd, une couche de graphène a été construite sur un substrat de palladium[START_REF] Murata | Orientation-dependent work function of graphene on Pd (111)[END_REF][START_REF] An | Large-Area Synthesis of Graphene on Palladium and Their Raman Spectroscopy[END_REF], par ségrégation et par dépôt chimique en phase vapeur. L'intercalation de palladium sous le graphène a également été réalisée sur différents substrats[START_REF] Huang | Intercalation of metal islands and films at the interface of epitaxially grown graphene and Ru (0001) surfaces[END_REF][START_REF] Yagyu | Neutralization of an epitaxial graphene grown on a SiC (0001) by means of palladium intercalation[END_REF]. Cependant, nous n'avons trouvé aucune étude des propriétés électroniques de tels systèmes hybrides Gr/Pd. La dispersion électronique d'une monocouche de palladium sur Ir(111) est d'abord étudiée, afin d'identifier ses bandes dans le voisinage des points K Gr et K Ir . Cette monocouche est caractérisée par deux états de puits quantiques, qui présentent une séparation en énergie allant de 120 meV au point K Gr à 170 meV au point K présente l'étude des systèmes hybrides Gr/PdCo. Les précédents chapitres ont montré qu'à la fois le cobalt et le palladium modifient la structure de bande du graphène. Dans cette partie, nous présentons une étude préliminaire de la co-intercalation de Co et Pd sous la couche de graphène, pour étudier la possibilité de plus amples modifications de la dispersion électronique du graphène. Pour éviter toute influence de l'ordre de déposition, nous réalisons pour la suite le dépôt et l'intercalation simultanés de cobalt et de palladium.Des mesures topographiques sur de tels systèmes sont actuellement réalisées par le Pr.

	La bande π du graphène s'élargit pour des recouvrements décroissants et son intensité diminue, comparée à celle des bandes du substrat. Un léger dopage (< 50 meV) est prob-ablement causé par la grande densité des bords de feuillets de graphène. Cependant, le cône de Dirac conserve ses caractéristiques principales (grande mobilité électronique, "minigap" dûs aux répliques du cône, presque pas de dopage) jusqu'à un recouvrement de 70%. Notre stratégie de croissance et d'intercalation "par le côté" est donc une option viable pour des mesures spectroscopiques d'ARPES. Une étude bibliographique des systèmes Co-Pd est tout d'abord présentée. Les alliages PdCo montrent une grande variété de structures selon leur composition, la température et leur dimensionnalité (volume, surface, nanoparticules). Pour de faibles dimensions (nanoparticules), une structure coeur-coquille est favorisée pour des températures in-Des mesures spectroscopiques d'ARPES préliminaires sont présentées. Nous nous con-centrons sur des compositions riches en palladium et les dispersions électroniques des deux échantillons Gr(70%)/Pd(80%)-Co(20%) et Gr(70%)/Pd(70%)-Co(30%) sont com-parées à celles du graphène et du palladium. Nous montrons qu'une petite quantité de cobalt (20%) modifie les états électroniques issus du palladium avec la disparition de férieures à 500 Mikhail Fonin et son équipe à l'université de Constance. deux états polarisés en spin vers -0.3 eV au point K

• C augmente légèrement la quantité intercalée, mais le motif du moiré devient moins résolu, suggérant la formation d'un alliage Co-Ir sous la couche de graphène. Afin d'augmenter l'efficacité de l'intercalation, nous nous tournons vers l'intercalation "par le côté" qui requiert de nombreux bords de feuillet de graphène. xiv L'élaboration est reliée à la morphologie locale de l'échantillon : les marches atomiques du substrat facilitant la nucléation du graphène, une grande densité de marches atomiques entraîne un grand recouvrement du graphène. Le recouvrement du graphène est aussi mesuré in situ par spectroscopie Auger (technique disponible dans notre laboratoire), et comparé avec les valeurs obtenues par STM. La qualité cristalline globale des échantillons est vérifiée par diffraction d'électrons lents (en anglais, low-energy electron diffraction, LEED). L'intercalation de cobalt et de palladium, respectivement, est réalisée sous une couche de graphène à recouvrement partiel. Les motifs des moirés sont comparés, et bien qu'ayant la même périodicité spatiale de 2.6 nm, le palladium intercalé montre une amplitude intermédiaire de 40 pm, confirmant une interaction avec la couche de graphène entre celle de l'iridium (faible) et celle du cobalt (forte). L'intercalation de 0.1 monocouche et 0.5 monocouche de cobalt est réalisée sous le graphène (recouvrement de 50%). Tout le cobalt déposé s'intercale, suggérant que les atomes intercalés sont énergétiquement favorisés, par rapport à ceux en surface, soit du graphène, soit du substrat Ir

[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]

. Le dépôt de 0.3 monocouche de palladium sur la même couche de graphène montre que le palladium s'intercale mais forme également des îlots bidimensionnels sur le substrat.

Pour augmenter la quantité de palladium intercalé, nous réduisons la surface libre du substrat en augmentant le recouvrement du graphène à 65%. Plusieurs dépôts successifs de palladium sont alors réalisés, les résultats sont analysés. Bien que des îlots soient toujours présents sur le substrat, l'intercalation complète de la couche de graphène est atteinte pour un dépôt de 0.9 monocouche. Pour la suite, nous déposerons une monocouche atomique pour s'assurer de l'intercalation complète de la couche de graphène.

Le graphène ne recouvrant pas toute la surface de l'échantillon et étant inhomogène, Résumé en francais xv il n'est pas évident qu'il présente la même structure de bande qu'une couche complète de graphène. Des mesures spectroscopiques (ARPES) de couches de graphène avec différents recouvrements sont donc effectuées, et comparées avec une couche complète.

Le chapitre 5 présente l'étude des propriétés électroniques des système hybrides Gr/Co. Nous commençons par présenter les mesures ARPES de systèmes hybrides Gr/Co déjà publiées

[START_REF] Vita | Electronic structure and magnetic properties of cobalt intercalated in graphene on Ir(111)[END_REF][START_REF] Pacilé | Electronic structure of graphene/Co interfaces[END_REF]

. Ces deux références présentent des mesures ARPES de, respectivement, 1 et 2 monocouches de cobalt intercalées entre une couche de graphène complète et le substrat Ir

[START_REF] Varykhalov | Ir(111) surface state with giant Rashba splitting persists under graphene in air[END_REF]

. Ces deux systèmes présenteraient alors un décalage de la bande π du graphène d'environ -2.5, -3 eV en-dessous du niveau de Fermi, et la présence d'états 3d du cobalt vers -1.5 eV. Cependant, la méthode de croissance employée dans ces publications est différente de notre travail. La couche de graphène a effectivement été conçue par dépôt chimique en phase vapeur, obtenant une couche complète de graphène et suggérant une intercalation "par dessus". De plus, l'intercalation du cobalt, après un dépôt à température ambiante, a été réalisée à des températures entre 500 • C et 600 • C, ne tenant pas compte de la formation d'alliage entre Co et Ir. Avant de comparer notre méthode de croissance avec celle de ces références, nous mesurons d'abord la dispersion électronique des systèmes non-intercalés (Ir(111), Gr/Ir(111) et Co/Ir(111)) afin d'identifier les bandes en jeu dans cette région de l'espace réciproque. En accord avec la littérature [62], le substrat Ir(111) est caractérisé par trois états de surfaces (S 1 , S 2 et S 3 ) et un état appelé I, dans le voisinage des points K Gr et K Ir . La couche de graphène présente un cône de Dirac intense, et les états du substrat sont encore visibles, bien que moins intenses. Une monocouche de cobalt est caractérisée par deux états additionnels : un état atteignant K Ir à -1.57 eV (Co1), qui disperse vers de plus hautes énergies dans la direction M Ir K Ir et reste plat sur K Ir Γ, et un état peu intense en-dessous de -4 eV (Co2). Lpeut-être possible de construire un alliage Co-Ir, riche en iridium, qui conserverait la dispersion du cône de Dirac, tout en induisant de légères modifications dues au Co. Pour étudier l'effet de l'alliage Co-Ir sur le cône de Dirac, nous déposons moins d'une monocouche de Co. Après l'intercalation de 0.6 monocouche de Co à 400 • C, les états du cobalt (Co1, Co2 et GrCo), ainsi que le cône de Dirac, inchangé, sont visibles, confirmant la présence de graphène non-intercalé. Un recuit supplémentaire à 650 • C change drastiquement la structure de bande de l'échantillon. Le cône de Dirac est toujours présent mais est fortement modifié par rapport au graphène isolé. Proche du niveau de Fermi, la vitesse des électrons (pente de la dispersion E( k)) augmente d'environ un facteur 2. À de plus basses énergies, la différence d'énergie entre le cône mesuré et celui du graphène isolé dépend du vecteur d'onde et est différente selon les deux directions de haute symétrie (M Gr K Gr et K Gr Γ). Aucun de ces effets n'étant présent pour une monocouche de cobalt intercalée à 650 • C, cette modification du cône de Dirac est reliée à la quantité de cobalt. L'alliage Co-Ir formé à cette température peut en effet avoir différentes structures selon sa composition. Le dépôt du cobalt à 400 • C, plutôt qu'à température ambiante, peut aussi jouer un rôle dans le procédé d'intercalation et la formation d'alliage. Le chapitre 6 présente l'étude des propriétés électroniques des sytème hybrides Gr/Pd. Une première étude bibliographique des systèmes hybrides Gr/Pd est présentée. Le palladium a majoritairement été étudié pour ses propriétés catalytiques. Le graphène, grâce à sa grande surface et sa stabilité chimique, est un bon candidat pour être le support d'une catalyse de surface. Dans ce cadre, des petites quantités de palladium xvii déposées sur une Ir . Des calculs dans le cadre de la théorie de la fonctionnelle de densité (en anglais, density functional theory, DFT) confirment que ces deux états sont polarisés en spin, par le couplage spinorbite du palladium. Tous les calculs de DFT de cette thèse ont été réalisés par le Pr. Elena Voloshina et le Pr. Yuriy Dedkov (Shanghai University). De plus, ces deux états polarisés se situent dans le voisinage du cône de Dirac du graphène. Une fois la monocouche de palladium intercalée entre le graphène et le substrat, le cône de Dirac est en effet fortement modifié. Le graphène est fortement dopé n, avec l'ouverture d'un "gap" (fossé énergétique) de 600 meV au point K Gr . De plus, la bande π du graphène est polarisée en spin, avec une séparation en énergie dépendante du vecteur d'onde, partant de 200 meV à 0.15 Å -1 du point K Gr et se réduisant fortement à l'approche du point K Gr . Ces résultats sont étayés par des calculs de DFT, qui démontrent que le mécanisme de la polarisation en spin du cône de Dirac est en effet un couplage spin-orbite intrinsèque induit par hybridation électronique entre le graphène et la monocouche de palladium. L'analyse menée dans ce chapitre entraîne deux conclusions fondamentales. Premièrement, le système graphène-palladium représente un modèle prometteur pour la réalisation de dispositifs spintroniques et pour l'étude de nouvelles phases quantiques, causées par la polarisation en spin du cône de Dirac. Plus généralement, l'approche envisagée d'adapter la dimensionnalité de métaux lourds, interfacés avec une couche de graphène, pourrait induire une séparation spin-orbite géante des états de valence du graphène. Deuxièmement, des états de puits quantiques existent dans de nombreux systèmes et pourraient exister pour d'autres monocouches atomiques sur un substrat. Si le graphène s'hybride avec de tels états, la séparation en spin induite dans ses états de valence pourrait être encore plus grande que celle mesurée dans cette thèse. Le chapitre 7 • C [69, 70]. Selon des calculs théoriques, cette structure coeur-coquille serait un coeur de Co et une coquille de Pd, mais les deux compositions ont été observées par dépositions successives de Co et Pd, le premier matériau déposé formant le coeur de la structure. Dans des systèmes plus grands, le Pd est situé préférablement proche de la surface à cause de son énergie libre de surface plus faible [71]. Avec ces informations, on peut s'attendre à ce que l'intercalation successive de Co et Pd à une température inférieure à 500 • C produise des nanostructures coeur-coquille. Au contraire, il est possible que, grâce à la faible mobilité des atomes intercalés, la co-intercalation de Co et Pd produise une formation d'alliage sans séparation de phase. Nous avons également cherché des publications scientifiques traitant de l'intercalation de plusieurs espèces sous le graphène, et n'en avons trouvé qu'une [72]. Dans ce travail, des petites quantités (inférieures à la monocouche) de fer et de cobalt sont intercalées successivement entre une couche de graphène et un substrat d'iridium. Les deux espèces intercalées sont différenciables par l'amplitude de leur moiré. Aucun alliage n'est observé, même lorque les deux espèces sont en contact sous la couche de graphène. Des mesures topographiques préliminaires de tels systèmes hybrides Gr/PdCo sont alors présentées. Après l'intercalation de 0.5 monocouche de Co sous une couche de graphène avec un recouvrement de 50%, un autre dépôt de 0.25 monocouche de Pd est réalisé. Les domaines intercalés présentent deux moirés différents : on retrouve le moiré précédemment observé de Gr/Co/Ir, et le second moiré présente une amplitude d'environ 100 pm, correspondant également à du cobalt intercalé. En revanche, ce dernier présente une symétrie d'ordre 3. Il semblerait donc que le palladium forme des ilôts bidimensionnels à la surface du substrat mais modifie l'interaction entre la couche de graphène et la couche de cobalt intercalée. Gr . Dans cette région, deux nouveaux états avec une dispersion linéaire apparaissent et ne correspondent pas au modèle de liaison forte du cône de Dirac du graphène. Bien évidemment, de plus amples expériences sont nécessaires pour comprendre l'effet de la co-intercalation de Co et Pd sur la structure de bande de graphène.

  The dispersion relation is E ± ( κ) = ± v F κ, with κ the momentum measured with respect to the Dirac point and v F the Fermi velocity. The most striking difference with the usual case of a parabolic metallic band E ± ( κ) = ±

	indeed a linear dispersion corresponding to relativistic, massless, chiral Dirac fermions.
	2 κ 2 2m * is that the Fermi velocity does not
	depend on the energy or momentum and is constant near the Dirac point. Moreover,
	the electrons move in graphene at a speed of v F	1 × 10 6 ms -1 , around 1/300 of the
	speed of light and almost 150 times faster than in silicium, justifying the great interest
	in graphene. The electrons in graphene are called "massless" and "relativistic" because
	of the graphene crystal symmetry (two equivalent carbon sublattices A and B) which
	makes the low-energy quasiparticles obey to a relativistic Dirac-like hamiltonian:
		2.1b)
	called Dirac points K (K') (fig. 2.1a)). At these points, the π band of graphene exhibits

Table 2 .

 2

1: Examples of SOC substrate-induced in graphene.

Table 4 .

 4

		ε 2p (meV) γ 0 (eV) s 0
	Typical values	0.0	-2.5, -3 0.0
	Complete Gr	4.9	-2.64	0.0
	TPG2	41.2	-2.68	0.0
	TPG3	36.8	-2.77	0.0

1: Calculated values of 1 st nearest-neighbor tight-binding model for TPG2, TPG3 and a complete Gr layer compared with typical values for a quasi-freestanding graphene

[START_REF] Reich | Tight-binding description of graphene[END_REF]

.

Table 5 . 1 :

 51 Measured slopes for both M Gr K Gr and K Gr Γ directions. The slopes correspond to the lines shown in figure5.10.

  5 ML of Co was completely intercalating under a graphene covering 50% of the sample surface (see fig. 7.4), when deposited at 400 • C. On the same sample, we deposited 0.25 ML of Pd at 400 • C to observe the behavior of the two intercalants. When looking at large scale images (fig. 7.5a)), most of the graphene is intercalated (red areas) and large metallic islands are laying on Ir(111) (gray areas). The situation is similar than the one after the Co deposition (fig. 7.4) with the addition of these islands, suggesting that the added Pd is forming 2D islands and is not intercalating under graphene. These 2D islands are pinned on the lower part of the substrate step edges and are in contact with several graphene flakes, even surrounding them completely

in some cases. However, at this scale, we don't retrieve enough resolution to discriminate the respective moiré of Gr/Co/Ir and Gr/Pd/Ir. Fig.

7

.6 therefore displays topographic images at a smaller scale.

Acknowledgements

First of all, I want to thank my advisors Dr. Dimitri Roditchev and Dr. Sergio Vlaic, and also Dr. Stéphane Pons who gave me the opportunity to work in their group on this fascinating project. I had the chance to take advantage of their scientific competencies to improve and develop my PhD project. I would also like to thank Dr. Véronique Brouet, Pr. Yannick Fagot-Revurat, Dr. Laurence Magot, Pr. Marko Kralj and Dr.

Matteo Calandra for accepting serving on the jury committee of this thesis.

A substantial part of my thesis was realized in collaboration with the team of Pr. Mikhail Fonin in the University of Konstanz (Germany). They welcomed me in their laboratory for one month and were very friendly and available. For that, I would like to thank Pr.

Mikhail Fonin and his PhD student Sabina Simon. I also would like to thank Pr. Elena Voloshina and Pr. Yuriy Dedkov of Shanghai University, and Pr. Beate Paulus and Kangli Wang of the University of Berlin, who provided every DFT calculations present in this work.

I am grateful to all the LPEM for the good and pleasant working environment. I thank all my friends from Paris (most of them also PhD students) for making me really enjoy these three years. It was really enriching to discuss our troubles around a beer or a diner. I thank also my older friends from Lyon and my family for the moral support and the unforgettable holidays.

Abbreviations

AES

performed to reduce the inhomogeneity of the sample. While a structural study of such co-deposited samples is currently realized by Pr. Mikhail Fonin in Konstanz, preliminary spectroscopic experiments reveal that the incorporation of Co atoms (low amount) in the intercalated Pd layer modifies the band structure of the hybrid system. The Pd(80%)-Co(20%) composition seems very promising, conserving the spin-separation of the Dirac cone, induced by the Pd intercalation, while novel states with linear dispersions appear at the Fermi level. Further investigations are required to achieve a full understanding of such Gr/CoPd systems. This thesis represents a first step towards the investigation of the electronic properties of graphene/metal hybrid systems where the metallic layer structure can be controlled at the nanoscale. Up to now the focus has been given on the interaction of graphene with single atomic layers composed by one or two elements.

In this respect several aspects have to be addressed in the following. First of all, a more detailed study of the CoPd intercalated samples has to be performed with the investigation of their structure and electronic properties as a function of the alloy composition.

The effect of increasing temperature should also be addressed.

Our study of Gr/Co hybrids revealed the key role of the intercalation temperature on the structural and electronic properties of the system with the formation of a Co/Ir alloy, under graphene, which provides a momentum dependent modification of the Dirac cone.

An extensive study of the effect of the Co-Ir surface alloy on the graphene electronic dispersion should be done, performing a more detailed analysis of the hybrid electronic properties as a function of the alloy structure and composition. Moreover, once the Co-Ir alloy is formed, the further intercalation of Pd could result in modifications of their interaction, achieving a different electronic dispersion.

An other aspect that should be addressed is the effect of the intercalated thickness on the electronic properties of the hybrid. The increase of the number of intercalated atomic layers would induce the relaxation of the metallic film [START_REF] Drnec | Surface alloying upon Co intercalation between graphene and Ir(111)[END_REF][START_REF] Carlomagno | Co film stretching induced by lattice mismatch and annealing: The role of graphene[END_REF]. The registry between graphene and the intercalant underlayer can therefore be tuned, allowing to tailor the lattice mismatch at the graphene/metal interface. This represents a key parameter for the electronic hybridization, since it strongly influences the overlap of the wave functions at the interface.

Appendix A

Data treatment: from angles to reciprocal space

This appendix is presenting in more details the data treatment made to go from the intensity matrix measured by the analyzer to the intensity matrix in the reciprocal space. Since the ARPES set-up has been installed at the beginning of 2016 during my PhD thesis, we developed the software to perform all the data analysis. In particular, I was in charge of this part of the program. A.1, the axis of the rotation matrices that describe the motion of the sample depend on θ and φ. We remind the formula of the rotation matrix R(α, u) by an angle α around an axis with unit vector u:

ABSTRACT

The discovery of graphene (Gr) has opened a fascinating research field with ultimate goal of using graphene as a building block for next generation electronics. Gr indeed exhibits an exceptionally high electron mobility, originating from a linear dispersion of its π band called Dirac cone. Spintronics, which exploits the coupling between the electron motion and their intrinsic magnetic moment, represents an emerging field predicted to lead to a technological revolution for data elaboration, and could widely benefit from graphene outstanding electronic properties. However, in graphene, electrons spins experience almost no coupling with electron motion and its all band structure is spin-degenerate. This situation changes dramatically when graphene is interfaced with other materials to form the so-called hybrid systems. In these kinds of systems, it is possible to engineer the graphene band structure inducing novel properties while preserving the natural high electron mobility of pristine graphene. Moreover, the graphene itself can strongly modify the physical properties of the material to which it is interfaced. These two effects make graphene-based hybrid systems extremely appealing to develop novel materials with desired properties.

The aim of this thesis is to explore how the graphene electronic properties can be modified by interface effects. More precisely, we focus on two interactions which could induce a spin-polarization of the bands forming the Dirac cone: exchange interaction and spin-orbit coupling. As model systems, we propose Gr/Palladium and Gr/Cobalt interfaces for studying respectively spin-orbit coupling and exchange interaction, both grown on an Ir(111) substrate. The desired hybrid systems are made by intercalation techniques, which provides high quality samples. The electronic properties are addressed by angle resolved photoemission electron spectroscopy giving access to the hybrid band structure.

In the case of Gr/Co hybrids, we show that the induced properties in graphene layer strongly depend on the sample preparation conditions. When Gr lies on pure Co the Dirac cone is destroyed while for Gr supported on a disordered CoIr alloy, the Dirac cone dispersion is preserved with an enhancement of the electron velocity at the Fermi level.

In the case of Gr/Pd hybrids we observe the emergence of spin-polarized split states near the Fermi level at the graphene K point. The spin splitting is energy and momentum dependent. Density Functional Theory calculations reveal that the spin-split bands are the result of intrinsic spin-orbit interaction originating from the Gr-Pd hybridization.

The addition of a small amount of Co atoms in the Pd intercalated film shows a further modification of the hybrid band structure with the appearence of novel linearly dispersing states at the Fermi level.

KEYWORDS

graphene -band structure -intercalation -photoemission -spin-orbit coupling