Xavier Marie

César González
email: cesar.gonzalez@ucm.es

Yannick J Dappe
email: yannick.dappe@cea.fr

Part of the Special Issue: Recent advances in 2D material physics

Keywords: Electronic structure, Defects, MoS 2, DFT, STM/AFM, Molecular adsorption Mots-clés. Structure électronique, Défauts, MoS 2, DFT, STM/AFM, Adsorption moléculaire

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Introduction

The rise of graphene and, in particular, the possibility of isolating one atomic layer from graphite, has participated to an important revolution in nanoelectronics [START_REF] Novoselov | Electric field effect in atomically thin carbon films[END_REF]. Indeed, graphene is wellknown now as a bidimensional material with fascinating electronic properties like high conductivity or massless Dirac fermions [START_REF] Voloshina | Graphene on Rh(111): scanning tunneling and atomic force microscopies studies[END_REF][START_REF] Xu | Scanning tunneling microscopy characterization of the electrical properties of wrinkles in exfoliated graphene monolayers[END_REF][START_REF] Castro Neto | The electronic properties of graphene[END_REF]. But in a second time, the discovery of graphene has also shed light on a whole world of new bidimensional materials. For example, hexagonal boron nitride (hBN) as the graphene counterpart made of boron and nitrogen is widely used due to its widegap and its encapsulation properties [START_REF] Han | Effects of hexagonal boron nitride encapsulation on the electronic structure of few-layer MoS 2[END_REF][START_REF] Liu | Hysteresis-free hexagonal boron nitride encapsulated 2D semiconductor transistors, NMOS and CMOS inverters[END_REF]. Also we have seen the emergence of the great family of transition metal dichalcogenides (TMDC), made of a transition metal layer sandwiched in between two chalcogen atom layers, and presenting several different properties [START_REF] Manzeli | 2D transition metal dichalcogenides[END_REF][START_REF] Nalwa | A review of molybdenum disulfide (MoS 2 ) based photodetectors: from ultra-broadband, self-powered to flexible devices[END_REF][START_REF] Giannazzo | Conductive atomic force microscopy of semiconducting transition metal dichalcogenides and heterostructures[END_REF][START_REF] Li | Two-dimensional MoS 2 : properties, preparation, and applications[END_REF]. Among the most common ones, we can consider metallic or semiconductor behaviors, superconductors, ferromagnets, etc. . . in other words, the full Solid State Physics can be found in these 2D materials [START_REF] Klein | Probing magnetism in 2D van der Waals crystalline insulators via electron tunneling[END_REF]. As such, these new materials open a wide spectrum of exciting perspectives for the development of nanoelectronics. For example, besides electronic properties, these materials present interesting thermal conductivity in the plane and at the interface between two layers, with important applications for thermoelectronic devices [START_REF] Zhang | Measurement of lateral and interfacial thermal conductivity of single-and bilayer MoS 2 and MoSe 2 using refined optothermal Raman technique[END_REF]. A dedicated theoretical study has revealed the important role of phonon scattering at the interface between the layers [START_REF] Zhang | Strong interfacial interactions induced a large reduction in lateral thermal conductivity of transition-metal dichalcogenide superlattices[END_REF].

Another important aspect lies in the fact that these materials can be combined to form new nano-architectures presenting different properties. Hence, exploiting the weak and van der Waals (vdW) interactions between these atomic layers, one can assemble different 2D materials and take advantage of the different properties to create new multielectronic devices [START_REF] Geim | Van der waals heterostructures[END_REF]. These assemblies are called van der Waals heterostructures, and constitute a very active field of research nowadays [START_REF] Liao | Van der Waals heterostructures for optoelectronics: progress and prospects[END_REF][START_REF] Li | Devices and applications of van der Waals heterostructures[END_REF]. Very recently, researchers have even developed new types of van der Waals heterostuctures, namely 1D van der Waals heterostructures [START_REF] Xiang | One-dimensional van der waals heterostructures[END_REF].

When considering electronic properties in whichever material, one cannot avoid the question of defects. Indeed, fabrication of materials implies necessarily the creation of defects. Even more relevant when growing 2D materials, it is clear that we will observe the creation of vacancies, atomic substitutions or atomic or molecular impurities adsorbed on the surface of the material [START_REF] Noh | Stability and electronic structures of native defects in single-layer MoS 2[END_REF][START_REF] Zhou | Intrinsic structural defects in monolayer molybdenum disulfide[END_REF][START_REF] Hong | Exploring atomic defects in molybdenum disulphide monolayers[END_REF]. Considering the low electronic density of such materials, such defects will obviously affect their electronic properties, for example by inducing metallic states or modifying the original electronic gap of the material. As a consequence, electronic transport properties or chemical reactivity might be modified [START_REF] Mondal | Unusual reactivity of MoS 2 nanosheets[END_REF][START_REF] Chen | Degradation behaviors and mechanisms of MoS 2 crystals relevant to bioabsorbable electronics[END_REF]. On another hand, one can think about exploiting these new induced properties to create new nanoelectronic devices. Indeed, starting from a well-known electronic material and modifying its atomic structure by creating controlled defects allows to shape its electronic properties in a desired direction. In that respect, a major challenge nowadays to control the creation of such defects is also an accurate characterization at the C. R. Physique -Online first, 25th May 2021 atomic level [START_REF] Zhou | Intrinsic structural defects in monolayer molybdenum disulfide[END_REF][START_REF] Hong | Exploring atomic defects in molybdenum disulphide monolayers[END_REF][START_REF] Mohan | Atomic adsorption of Sn on mechanically cleaved WS2 surface at room temperature[END_REF]. Such a characterization can rely on atomic probe microscopies such as Scanning Tunneling Microscopy (STM) or Atomic Force microscopy (AFM) which allow us to characterize the local electronic density or the local atomic forces. Indeed, conductance or force measurements are very useful to determine a local chemical environment and its subsequent incidence on the electronic properties [START_REF] Sørensen | Structure and electronic properties of in situ synthesized single-layer MoS 2 on a gold surface[END_REF][START_REF] Santosh | Impact of intrinsic atomic defects on the electronic structure of MoS2 monolayers[END_REF][START_REF] Kodama | Electronic states of sulfur vacancies formed on a MoS2 surface[END_REF]. However, these techniques are rather complex to interpret and the help of theory and modelling is often welcome to ensure a good understanding of the acquired results. For example, Density Functional Theory (DFT) calculations allow a modelling at the atomic level with a high accuracy on the electronic properties, providing an excellent support to experimental results [START_REF] Makarova | Selective adsorption of thiol molecules at sulfur vacancies on MoS 2 (0001), followed by vacancy repair via sâc dissociation[END_REF][START_REF] Komsa | Native defects in bulk and monolayer MoS 2 from first principles[END_REF].

To illustrate this approach, we present here a mini-review of our recent results on atomic defect simulations in 2D materials. We consider here the well-known molybdenium disulfide (MoS 2 ), which is a 2D semiconductor presenting the peculiar characteristic of having a direct gap in the monolayer phase, and an indirect gap for thicker films. This material originally used as a lubricant for engines since decades is very promising for nanoelectronics and optoelectronics applications [START_REF] Thamankar | Low temperature nanoscale electronic transport on the MoS 2 surface[END_REF][START_REF] Zhao | Gas adsorption on MoS 2 monolayer from first-principles calculations[END_REF][START_REF] Froehlicher | Direct versus indirect band gap emission and exciton-exciton annihilation in atomically thin molybdenum ditelluride (MoTe 2 )[END_REF]. Also, besides some Scanning Transmission Electronic Microscopy (STEM) or STM experiments, rather few studies of atomic or substitutional defects have been performed on this material [START_REF] Zhou | Intrinsic structural defects in monolayer molybdenum disulfide[END_REF][START_REF] Hong | Exploring atomic defects in molybdenum disulphide monolayers[END_REF]. In particular, on a theoretical point of view, an exhaustive study of defects in MoS 2 was clearly missing.

The organization of the article is the following: in the next section, we will present the main results obtained on the modelling of atomic and substitutional defects in MoS 2 . Starting from the pristine MoS 2 , we will consider the main possible defects like Mo or S vacancies, and we will address them by STM images modelling, through electronic conductance calculations, and AFM modelling through force calculations. In Section 3, we will consider these defects under the angle of molecular adsorption, in particular to check the reactivity of the defects and to determine how the molecules affect the electronic properties. Section 4 will be devoted to new calculations on lateral MoS 2 junctions: we consider a defective MoS 2 nanoribbon sandwiched between gold electrodes and we determine the corresponding conductance, to be compared with the vertical conductance discussed in Section 2. Finally, we conclude and bring some perspectives on this general topic.

Point defects in a MoS 2 monolayer

In this section, we will consider the main potential point defects in a layer of MoS 2 through STM and AFM modelling. First, we start with pristine MoS 2 , in order to present the general characteristics of this system and to present briefly the computational method used here.

Pristine MoS 2

For all the calculations presented here, described in full details in Ref. [START_REF] González | Theoretical characterisation of point defects on a MoS2 monolayer by scanning tunnelling microscopy[END_REF], we have considered a 6×4 rectangular unit cell of MoS 2 (72 atoms), as represented in Figure 1(a). Calculations including structural relaxations and electronic structure determination have been performed using the very efficient DFT localised-orbital molecular dynamics package FIREBALL [START_REF] Lewis | Advances and applications in the FIREBALL ab initio tight-binding molecular-dynamics formalism[END_REF][START_REF] Jelínek | Multicenter approach to the exchange-correlation interactions in ab initio tight-binding methods[END_REF][START_REF] Sankey | Ab initio multicenter tight-binding model for molecular-dynamics simulations and other applications in covalent systems[END_REF]. This code is based on a self-consistent version of the Harris-Foulkes functional, which allows to perform the self-consistency over the occupation numbers [START_REF] Harris | Simplified method for calculating the energy of weakly interacting fragments[END_REF][START_REF] Foulkes | Tight-binding models and density-functional theory[END_REF]. Also, the exchange correlation energy is calculated according to the multi-centre weighted approximation (McWEDA, which corresponds to an LDA formalism in the Harris-Foulkes functional) [START_REF] Jelínek | Multicenter approach to the exchange-correlation interactions in ab initio tight-binding methods[END_REF]. Finally, FIREBALL uses a localized optimised basis set [START_REF] Basanta | Optimized atomic-like orbitals for first-principles tight-binding molecular dynamics[END_REF] and we have used cutoff radii (in atomic units) of s = 3.1 and 6.2, and p = 3.9 and 6.2 for S and Mo respectively, and d = 5.8 for Mo. z orbitals (blue uptriangles), in-plane p x +p y (down-triangles) and the sum of the other four d orbitals (yellow hexagons). Reprinted with permission from Ref. [START_REF] González | Theoretical characterisation of point defects on a MoS2 monolayer by scanning tunnelling microscopy[END_REF], copyright IOP 2016.

First, we have optimized the geometry of the pristine MoS 2 using the 6 × 4 unit cell, until the forces have reached a value lower than 0.05 eV/Å. From this optimized geometry, we have calculated the Density of States (DOS) of the system, and its different contributions from the different Mo and S orbitals, as represented in Figure 1(b-d). As a result, we can observe an electronic gap around 1.7 eV, mostly dominated by the electronic contribution of Mo. Taking a closer look at the different orbital contributions, we can deduce that the valence band is mostly dominated by Mo s + p z + d 2 z orbitals, and in a minor amplitude, other Mo d states. Also, the conduction band is dominated by the other d orbitals of Mo. On another hand, S atoms contribute to the valence and conduction bands mainly through their p x + p y states.

From this electronic structure, adding an atomic tip to the system to mimic the STM experiment, for example a 35-gold atoms pyramid [START_REF] González | Theoretical characterisation of point defects on a MoS2 monolayer by scanning tunnelling microscopy[END_REF], we can now simulate the corresponding STM image of the pristine MoS 2 , in order to set a reference to compare with defect calculations or further experimental results. To this end, the STM current is calculated based on the Keldysh-Green formalism, which uses the DOS of the STM tip (ρ T T ), the DOS of the system (ρ SS ) considered (MoS 2 here), and the tip-sample interaction (hoppings T T S/ST ) extracted from the Calculated STM images at 4.5 Å and a bias of (a) -0.1 V and (b) +1.9 V for a clean MoS 2 monolayer. The STM images were graphed using WSxM software [START_REF] Horcas | WSXM: A software for scanning probe microscopy and a tool for nanotechnology[END_REF]. Reprinted with permission from [START_REF] González | Theoretical characterisation of point defects on a MoS2 monolayer by scanning tunnelling microscopy[END_REF], copyright IOP 2016.

Fireball calculations. In that respect, the calculated current at 0 K temperature is expressed as:

I = 4πe 2 h E F +eV E F Tr[T T S ρ SS (ω)D r SS (ω)T ST ρ T T (ω -eV )D a T T (ω -eV )]dω, (1)
where D a T T and D r SS are complex matrices corresponding to multiple scattering effect produced by the possible electronic reflections occurring when the tip is close to the sample. Of course, at standard STM distances, these matrices are equal to identity and disappear from the formula. Finally, a full description of the methodology can be found in [START_REF] González | Theoretical study of carbon-based tips for scanning tunnelling microscopy[END_REF]. As a result, we present in Figure 2 the calculated STM images for pristine MoS 2 at (a) negative voltages, probing occupied states, and (b) positive voltages, probing unoccupied states.

The main important feature, is that at negative voltage, we only observe sulfur atoms, meanwhile at positive voltages, we can observe sulfur and molybdenium atoms. This is due to the effect of the STM tip-atom distance combined with the DOS contributions calculated previously. Indeed, at negative voltages, both S and Mo DOS are equivalent, but the tip-Mo distance is larger than the tip-S, wich favors the emergence of the S DOS in the STM image. Oppositely, at positive voltages, we have the same distance ratio, but the DOS of Mo is much larger than the one of S, which compensates the distance and makes the two types of atoms contribute to the STM images. This result can be understood in terms of the electronic hopping (T ST and T T S matrices in (1)). It measures the probability of an electron to jump between the tip and the sample. These values decrease exponentially with the distance, reducing drastically the contribution of the atoms at lower positions even though they can present much larger DOS. Consequently, we can deduce that the STM image gives us information not only on the respective DOS of the probed atoms, but also on their respective positions, even at different heights.

In the next subsection, we will see how we can use STM to characterize the main types of point defects in MoS 2 .

Defective MoS 2 : Scanning Tunneling Microscopy and conductances

The main point defects that we have considered here are related to Mo and S vacancies, and their respective antisites through atomic substitutions [START_REF] González | Theoretical characterisation of point defects on a MoS2 monolayer by scanning tunnelling microscopy[END_REF]. Namely, we consider Mo vacancy, S vacancy, S divacancy, and the corresponding substitutions like one or two S in a Mo vacancy, a Mo in a S vacancy, and one or two Mo in a S divacancy. These defects are very common in MoS 2 The formation energies have been calculated using the energy in a perfect Mo or S bulk. Reprinted with permission from Ref. [START_REF] González | Adsorption of small inorganic molecules on a defective MoS 2 monolayer[END_REF], copyright RSC 2017.

growth and can also be controlled in a rather easy manner by removing atoms. For a monolayer formed by N Mo and N S atoms, the formation energy can be expressed as [START_REF] González | Helium bubble clustering in copper from first principles[END_REF]:

E f = E t -N Mo E (Mo) -N S E (S) (2)
E (Mo) and E (S) are the atomic energies of a single Mo or S atom respectively, in a perfect Mo or S bulk, and E t is the total energy of the system. These formation energies have been calculated using the DFT-plane wave Vienna Ab initio Simulation Package VASP code [START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF][START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF], based on the pseudopotential approximation following the projector augmented wave (PAW) approach. More technical details about the calculations can be found in Ref. [START_REF] González | Reactivity enhancement and fingerprints of point defects on a MoS 2 monolayer assessed by ab initio atomic force microscopy[END_REF]. The corresponding results are presented in Table 1.

From these results, we can observe that the S vacancy presents the lowest formation energy (2.57 eV), which makes it very favorable to appear during the MoS 2 growth process, in good agreement with experiments [START_REF] Hong | Exploring atomic defects in molybdenum disulphide monolayers[END_REF]. Also, the formation energy of the S divacancy is twice the one of the S vacancy, meaning that it is the same cost to remove two S atoms independently. Comparatively, the creation of one Mo vacancy presents a formation energy of 7.22 eV, much higher, which is representative of the strong Mo-Mo bonding in MoS 2 . Overall, a general trend lies in the stability of these defects, which has also been probed using Molecular Dynamics simulations [START_REF] González | Adsorption of small inorganic molecules on a defective MoS 2 monolayer[END_REF], and which makes them promising system to consider for nanoelectronics applications.

The corresponding calculated STM images are represented in Figure 3. Looking at the images, a first point we can stress is that the global MoS 2 network is not drastically affected by the Mo or S vacancies. Indeed, apart when substituting the atoms, we observe more dangling bonds, with brilliant density trace in the STM image, than real surface reconstruction. For example, we can observe brilliant traces in the neighborhood of the missing atoms in Figure 3(a), (d) and (f), corresponding respectively to Mo, S and two S vacancies. As a consequence, we can expect from these dangling bonds an important local reactivity, making these sites very favorable for molecular adsorption, as we will see in the next section. Also, these changes in the local electronic density are obviously reflected in the electronic gap. Hence, in all the cases considered here, the gap is reduced from the pristine MoS 2 gap of 1.7 eV, to 1.0 eV in the S vacancy structure, 0.8 eV in the S divacancy, around 0.6 eV in the Mo and S substituted Mo vacancy, and no more gap for the other structures. This is attributed to the emergence of new states in the original gap, namely dangling bonds in vacancy configurations, or extra localized states in atomic substitutions. In particular, in the cases where the gap fully disappears, the substitution of S atoms in the S monoor divacancies by Mo atoms induces new metallic states that fill the electronic gap. These states are mainly of d 2 z character, originating of course from the substituting Mo atoms. They can be observed in the calculated DOS of Ref. [START_REF] González | Theoretical characterisation of point defects on a MoS2 monolayer by scanning tunnelling microscopy[END_REF] and can be attributed to the non-passivation of the substituting Mo atoms. It has to be noted that two S substitutions in a Mo vacancy yields a halfoccupied state at the Fermi level, and a gap of 1. [START_REF] Santosh | Impact of intrinsic atomic defects on the electronic structure of MoS2 monolayers[END_REF] The STM images were graphed using the WSxM software [START_REF] Horcas | WSXM: A software for scanning probe microscopy and a tool for nanotechnology[END_REF]. Reprinted with permission from Ref. [START_REF] González | Theoretical characterisation of point defects on a MoS2 monolayer by scanning tunnelling microscopy[END_REF], copyright IOP 2016.

tries to mimic the original MoS 2 structure, which sets the S atoms in the plane. Therefore, there is no additional corrugation in the system by substituting S atoms to the original Mo atoms. The main difference between S mono-and divacancy lies in the reactivity of the site, the removing of a second S atom leading obviously to more dangling bonds. In addition, the substitution of 2 S atoms by two Mo atoms leads also to a more metallic site.

This study reveals that the STM images of defective MoS 2 are strongly affected by the geometry of the system, even though the MoS 2 network surrounding the defect remains globally unaffected. Hence, the removal of Mo or S atoms induces protrusions associated to dangling bonds while the substitution of these atoms add metallic states and reduce the gap. The method developed here is anyway very powerful, as the images at different biases can be analyzed, in conjunction with the calculated DOS, in quest for specific peaks which constitute the fingerprint of the considered defect. Hence, this tool complements the experimental measurements, and it has been used as such for example in the discrimination of a nitrogen atom substitution in a S vacancy in a MoS 2 layer probed by STM [START_REF] Dubey | Weakly trapped, charged, and free excitons in single-layer MoS 2 in the presence of defects, strain, and charged impurities[END_REF]. Obviously, more complex defects like grain boundaries [START_REF] Barja | Charge density wave order in 1D mirror twin boundaries of single-layer MoSe2[END_REF][START_REF] Liu | Remarkably high thermal-driven MoS 2 grain boundary migration mobility and its implications on defect healing[END_REF] or molecular adsorption as we will discuss in the next section, can also be characterized using the same method. Finally, this study also reveals the potential ability of defects in MoS 2 for future nanoelectronics, through the local semiconductor/metal transition, or gas sensors upon molecular adsorption, which both affect the local DOS, and that can be detected through electronic conductance measurements. To illustrate this perspective, in the last section of this article, we propose a model of lateral MoS 2 junction sandwiched between two gold electrodes, where the electronic conductance of the system is measured and varies as a function of the considered defect.

In the next subsection, we will consider another type of local probe spectroscopy, namely force measurements through AFM, to further characterize defects in MoS 2 .

Defective MoS 2 : Atomic Force Microscopy and forces

Besides STM measurements which give us access to the local DOS of a system, a complementary spectroscopy lies in AFM experiments, and in particular non-contact AFM, which give us access to the local forces of a system. Obviously forces and local density are related, but the determination of the local forces brings different kind of information on a system. Indeed, we will show here that the defects induce an enhancement of the local reactivity, which is of paramount importance for atomic or molecular adsorption and applications in nanoelectronics.

Here we have considered the same atomic unit cell as for the STM study. However, we have optimized these cells and calculated the forces using VASP [START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF][START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF] instead of Fireball. In order to simulate an AFM experiment, we use two type of AFM tips, similarly to the STM tips used for the STM simulations, namely a very reactive Cu one and a much less reactive Si tip. Then the tip has been rigidly approached to the MoS 2 substrate, either pristine or defective, by steps of 0.25 Å, and the system has been fully optimized until the atomic forces reached a value lower than 0.025 eV/Å. The energy curve is then recorded for all the positions, and its derivation leads to the force curves that we use to analyze the different defects here.

The results of force calculations for the different defects and the two types of tips are presented in Figure 4.

As such, Figure 4(a) and (b) represent an atomic picture of the motion of the AFM tip in a Mo vacancy (Cu tip) and S vacancy (Si tip), respectively. This reveals the strong interaction that can occur, leading even to atomic capture. In Figure 4(c-e), we represent the typical force evolution as a function of the tip-surface distance, for different defects in MoS 2 , for the Cu tip, and the same for a Si tip in Figure 4(f-h). In these curves, we look for the minimum, namely the maximal strength of the force (corresponding to the maximal attraction), which is representative of the reactivity of the probed site. Obviously, as the tip approaches the sample, the minimum will be shifted according to the local reactivity of the site, through dangling bonds or local electronic densities, which will change depending on the type of defects and their chemical characteristics. For example, using a Cu tip on the pristine MoS 2 , the difference of force minimum for Mo and S atoms is about 0.7 Å, with very similar forces, i.e. -1.00 nN and -0.88 nN for S and Mo respectively [START_REF] González | Reactivity enhancement and fingerprints of point defects on a MoS 2 monolayer assessed by ab initio atomic force microscopy[END_REF]. This difference is explained by the contact difference between the two atoms, since for the S atom we have a direct Cu tip-S atom contact, whereas for the Mo atom, this contact is somehow screened by the neighboring S atoms. Also, we have to bear in mind that the choice of the tip is of high importance to characterize the probed system. Indeed, when determining the interaction forces using a Si tip which is known to be much less reactive, we will obtain this time a higher signal for the Mo atom than for the S atom, due to the establishment of a semiconductor-metal junction that we will discuss later. This explains also why we might obtain different force values with respect to previous results using different kind of AFM tip [START_REF] Ondráček | Forces and currents in carbon nanostructures: are we imaging atoms?[END_REF].

Turning to the different defects in MoS 2 , we first consider the result with the Cu tip. We can immediately notice a strong increase in reactivity through the different force minima for the different defect sites. Hence, in Figure 4(c-e), corresponding respectively to the S, Mo and two S vacancies, we have an important force minimum, the most important one corresponding to the Mo vacancy with a deviation of about -3.42 nN. In that respect, this very reactive Mo vacancy also presents some exotic effect as the ability of trapping atoms from the tip. This property is illustrated in a snapshot extracted from the simulations in Figure 4(a) where two Cu atoms remain trapped in the Mo vacancy site. This opens the way to specific doping through the use of AFM tip on MoS 2 defects and the creation and control of specific electronic defects. This atomic transfer has been already discussed in other material [START_REF] Custance | Atomic force microscopy as a tool for atom manipulation[END_REF][START_REF] Sugimoto | Complex patterning by vertical interchange atom manipulation using atomic force microscopy[END_REF] and is revealed here for 2D materials. Also, what is really interesting is the atomic substitution in MoS 2 vacancies, where a reduction of the reactivity, through the reduction of the forces, is observed. This can be understood through the saturation of the vacancy dangling bonds by the incoming atom for example. Of course the corresponding minima are also shifted due to the specific positions of these new substituting atoms.

A similar analysis can be achieved using a Si tip, which is much more flexible than the Cu tip, and therefore able to explore the defects in an easier manner. Considering the curves presented in Figure 4(f-h), we can observe in general much lower forces compared to the Cu tip, in particular for the interaction with S atoms. This is due to the lower reactivity of the Si tip, as explained before. However, for the defect with Mo substitutional atoms, we recover a strong increase of the tip-atom forces. For example the substitution of two S by two Mo in the S divacancy defect leads to a force of -2.55 nN, twice the value obtained using the Cu tip. We can also observe more important deformations of the tip, compared to the Cu tip, as a result of the higher flexibility of the Si tip.

In all the cases, we can deduce that the interaction is driven by a standard metalsemiconductor junction. Indeed, the Cu tip is more sensitive to S atoms, whereas the Si tip is more sensitive to the Mo atoms. In both cases, an important charge transfer between the two materials is responsible for the emergence of high forces. In that respect, one has to carefully consider the choice of the AFM tip material in order to carefully image one specific defect or another. Hence, the accurate visualization of a defect fingerprint is closely related to the choice of the AFM tip, either metallic or semiconductor.

In the next section, we will consider the influence of the defect reactivity on the molecular adsorption, and the consequences on their electrical conductance.

Molecular adsorption on MoS 2 defects and influence on the conductance/force properties

As we have seen in the previous sections, we now know how to discriminate different types of point defects in a MoS 2 layer using different probes like STM or AFM. Moreover, it is possible to have a measure of the local reactivity, through its incidence on the local conductance or on the local forces. In this section, we will consider the adsorption of small molecules on these defects and how they affect the electrical conductance or the local forces. This aspect is very interesting, first in order to probe the reactivity of the defect studied before, but also, in order to design new types of electronic nanodevices, or even gas sensors whose electrical conductance would be affected by the adsorption of a small molecule. This section is divided in two subsections, where we will first consider the adsorption properties, and then their consequences on conductance and forces.

Molecular adsorption as a probe for local reactivity

We have considered here small inorganic molecules, with size comparable to the size of the point defects considered in this study. Hence, we have performed DFT calculations to characterize the adsorption of CO 2 , CO, H 2 O, NO, NO 2 , H 2 and N 2 , on pristine and defective MoS 2 [START_REF] González | Adsorption of small inorganic molecules on a defective MoS 2 monolayer[END_REF]. The adsorption energy E Ads is defined as:

E Ads = E tot -E MoS 2 -E Mol (3)
where E tot is the total energy obtained with VASP for the system containing both the MoS 2 supercell and the molecule, and E Mol and E MoS 2 are the energies of the isolated molecule and MoS 2 rectangular supercell as defined previously, respectively. At first we consider pristine MoS 2 which is poorly reactive. In that respect, the molecular adsorption is driven by van der Waals interaction [START_REF] Patil | Adsorption of common solvent molecules on graphene and MoS 2 from first-principles[END_REF], and its inclusion in the calculations is of paramount importance. Unfortunately, this is not very convenient for designing electronic devices, as the molecules are very mobile in that configuration, with a high probability of diffusion with the temperature. For example, if we consider a CO 2 molecule on pristine MoS 2 , we obtain an equilibrium distance of 3.40 Å, for an adsorption energy of about -0.15 eV. This is in agreement with previous calculations on a large range of small molecules [START_REF] Wang | Electronics and optoelectronics of twodimensional transition metal dichalcogenides[END_REF][START_REF] Myoung | Large current modulation and spin-dependent tunneling of vertical graphene/MoS 2 heterostructures[END_REF][START_REF] Aguilar | Theoretical insights into CO 2 adsorption by MoS 2 nanomaterials[END_REF]. Consequently, we turn now to the study of molecular adsorption on the MoS 2 defects that we have considered in the previous sections. In Tables 2 and3, we present respectively the adsorption energies and equilibrium distances determined in DFT+vdW for a series of small inorganic molecules adsorbed on different MoS 2 defects.

From these results, we can deduce a general trend which is that the most reactive defects for molecular adsorption are the metallic ones, namely the S mono-or divacancy with one or The sites labelled with * correspond to the dissociative cases. Reprinted from Ref. [START_REF] González | Adsorption of small inorganic molecules on a defective MoS 2 monolayer[END_REF], copyright RSC 2017. two Mo substitutions. In particular, we can observe that the CO 2 molecule remains physisorbed for all the S or Mo vacancies, and increases drastically its adsorption energy in contact with 2 Mo substitutions in a S divacancy, which is the most interacting adsorption site for almost all the molecules. This is due to the metallic states that close the electronic gap of MoS 2 or to the metallic states located very close to the Fermi level. In that respect, a strong bonding is established between the substituting Mo atom and its metallic states, and the inorganic molecule. Also, we have determined the charge transfer between these metallic defects and the molecules and have found that it is not very important, around 0.04 e, in particular for CO 2 or CO molecules. This means that these molecules are very stable upon adsorption on the MoS 2 layer, and that they can be imaged or characterized through STM or AFM. As explained in the previous section, this adsorption process on metallic defects is favored by a metal-semiconductor junction, which appears to be very important for the understanding of defects in TMDC. Also, we can stress the fact that homonuclear diatomic molecules like O 2 , N 2 and H 2 present slightly different behavior with for example higher charge transfers, around 0.25-0.35 e. Finally, we have considered dissociation processes on MoS 2 defects, as a probe for MoS 2 catalytic activity. We have found for example, that molecules containing oxygen (CO 2 , NO 2 , . . . ) present a certain ability to dissociate on S vacancies at room temperature. The O atoms have the same electronic configuration as the S atoms, favouring their absorption in the S-vacancies. This obviously opens many promising perspectives for applications in gas storage or gas sensors. Now that we have characterized the adsorption process of molecules on MoS 2 defects, we will consider the implications on conductance and force measurements.

Conductances and forces on molecular adsorbed on defective MoS 2

Here we will consider the most reactive site for molecular adsorption on MoS 2 , as described earlier, which is the S divacancy with two Mo substitutions. As we have seen before, the small inorganic molecules are strongly bonded on this site, and therefore we can measure their conductance or forces by approaching a STM or AFM tip [START_REF] González | Molecular detection on a defective MoS 2 monolayer by simultaneous conductance and force simulations[END_REF]. This method aims at developing a new way to detect molecules on very reactive sites. In Figure 5, we present the evolution of the calculated forces and electrical conductance, as a function of the tip-molecule distance, for the different molecules discussed previously, adsorbed on the two Mo substituting S divacancy.

The first important aspect that we can deduce from these results, is that the combination of conductance and force measurements for each molecule adsorbed on the reactive site, constitutes a clear signature of the molecule. Indeed, considering to discriminate these systems based on force or conductance curves only might result very complicated and confusing as some results are really close. However, the combination of both is much more powerful. For instance, considering the force curves presented in Figure 5(a), we can observe different intensities through the minimum of the curve, each at a specific tip-molecule distance. This represents one clear fingerprint of the system. The most important force is then obtained for the N 2 molecule, with around -1.50 nN, at an apex distance of around 3.1 Å. Another clear fingerprint is extracted from conductance measurements, with the maximum conductance plateau and its value. For example, the highest conductance is obtained here for the H 2 O molecule, with 1.1 G 0 . Also the shape of the conductance is indicative, as some curves grow monotonically (H 2 O, CO 2 , . . . ) whereas others present a clear step of conductance before reaching the plateau (CO, NO, N 2 , . . . ). Also, homonuclear molecules present the same conductance (O 2 , N 2 ) whereas heteronuclear ones present a different value (NO), which facilitates their discrimination. Obviously, as we have discussed before, the chemical nature of the tip will have an influence on the obtained results, either on the force measurements (example of reactive Cu tip versus non-reactive Si tip), or on the conductance measurements through the work function of the material. Therefore, one has to use the same tip to probe the different molecules through conductance and force measurements. Clearly, this is a hard task to keep the same tip for different measurements on different systems, however the measurements in a specific range of forces and conductance should be sufficient to provide a general trend in order to identify the adsorbed molecule fingerprint.

In the next and final result section, we will consider another way to characterize MoS 2 defects or adsorbed molecules on MoS 2 defects through the use of lateral junctions and lateral conductance measurements.

Lateral junctions: conductance calculations

In the previous sections, using DFT we have modelled several types of defect in MoS 2 , as well as molecules adsorbed on these defects. In that respect, we have simulated the corresponding STM images and we have determined the forces that we can compare to AFM experimental measurements. Also, we have determined the conductance, and together with the force, we have seen that it can be assigned to a specific adsorbed molecule, through its particular fingerprint. Hence, we have developed a method which together with experimental results, allows to characterize specific point defects on the MoS 2 monolayer, and to conceive nanodevices or gas sensors. In this last section, we present new results where we consider defective MoS 2 nanoribbons, sandwiched between two gold electrodes. Hence, we now consider lateral junctions of defective MoS 2 , meaning that the MoS 2 nanoribbon is connected in the plane, on two sides of the nanoribbon, and not perpendicularly as in the case of STM or AFM experiments. This geometry is a bit different from the one we considered before when we have probed point defects using STM or AFM. The present geometry resembles what is used in nanoelectronic devices. In this case, we do not probe anymore the conductance between the tip and a defective 2D material, but we fully probe the electronic transport in the plane of the bidimensional material. It is therefore very interesting on a fundamental point of view. Also, in order to design gas sensors for example, this geometry is more adapted, since we do not need a STM or AFM apparatus to characterize the defect. A simple current measurement should give us access to the modification of the sensor in case of adsorbed gas. Some examples of these lateral junctions unit cells are presented in Figure 6.

We have considered here the same defects as those previously studied, and enlarged the unit cell in the electrode direction to avoid direct electrode coupling. The direction perpendicular to the electrode remains periodic. Hence, we have in Figure 6 As a result, we represent in Figure 7 the evolution of the electrical conductance for each defect configuration.

At first, we can observe that generally speaking, the calculated lateral conductances are much higher than their vertical counterpart when we were calculating the local conductance for the system in interaction with a STM tip. For example, the conductance of the defect formed by two Mo atoms in a S divacancy in MoS 2 with a O 2 , CO, or NO molecule adsorbed on top lies around 0.37-0.44 G 0 , whereas they were about 0.13-0.18 G 0 when probed by a STM tip. The only exception is the water molecule on the Mo substitution on the S divacancy defect in MoS 2 , which presents a conductance of 0.3 G 0 , whereas it reaches almost 1.0 G 0 when probed by a STM Cu tip. On another hand, the defect presenting the highest conductance, and with the biggest difference with respect to clean MoS 2 (about 0.52 G 0 ), is the Mo vacancy with a conductance of almost 0.7 G 0 . This might be exploited for nanoelectronic devices, since the electronic response is increased by about 40%. Surprisingly, a S vacancy saturated with Mo substituent or a S divacancy saturated by two Mo substituents present very similar electrical responses, with a conductance around 0.42 G 0 . In that respect, the adsorption of small molecules on these defects does not affect really the overall conductance, except for NO 2 , which helps reaching the conductance of clean MoS 2 , and NO, H 2 and H 2 O which lower the conductance until 0.35 G 0 . Again, a water molecule on two Mo in a S divacancy defect yields the lowest conductance. All in all, two Mo atoms in a S divacancy constitutes a rather promising gas sensor for NO 2 , NO, H 2 O and H 2 . Obviously, additional cases should be tested with different molecules on different defects, like the evolution of the Mo vacancy upon molecular adsorption for example, but our aim here is only to present the proof of concept of a potential method for gas sensing.

The conductance difference between vertical and lateral conductance is probably due to the bottleneck of the electric current at the interface between the tip and the molecule. Obviously the transport mechanism is rather different here, since we are probing electronic states in the gap of the MoS 2 , and we consider the propagation of the current all along the nanoribbon. Intuitively, we can consider that the introduction of metallic states in the gap (as it is obtained by the substitution of the two Mo atoms in the S divacancy) will favor the electronic transport in the MoS 2 nanoribbon. Also, we have to take into account the fact that the limits of the nanoribbon connected to the gold electrodes will create new states in the MoS 2 gap and affect the global electronic structure. In that respect, we present in Figure 8 the electronic transmission for different defects considered here.

As we can observe, the electronic structure of MoS 2 is greatly affected by the nanoribbon shape, introducing a strong localized state at the Fermi level for all the defective nanoribbons. These results show that there is no more gap in these MoS 2 nanoribbons, so the effect of the edges is still important for this size. Hence, the variation of conductance presented in Figure 7 is related to the localization of this peak in the vicinity of the Fermi level. Indeed, for clean MoS 2 , the peak is located just below the Fermi level, as for the common S vacancy, which explains the very similar conductance. Also, this means that the S vacancy does not affect drastically the electronic transport in the MoS 2 nanoribbon. On the other side, the Mo vacancy presents a peak slightly shifted toward the positive energies. This is easily understandable as the removal of a metallic atom induces a slight p doping in the system. In that respect the conductance is much higher at the Fermi level due to the crossing of the peak. However, taking a look at the T(E) curves, we can infer that probably the inclusion of a voltage would increase the difference between the different defects.

Conclusions and perspectives

To summarize, we have presented here a mini-review on our exhaustive work on defects in a MoS 2 monolayer. Using DFT calculations, we have defined and characterized these defects, mainly based on Mo and S vacancies, and their substitutional atoms. In particular we have determined their structure and formation energies, and shown the modulation of the local electronic properties through electronic gap reduction or emergence of very reactive metallic states in the gap. Then, we have modelled the corresponding STM images, in order to establish comparison with and to interpret future experimental results. We have shown in particular how a nitrogen substitution in a S vacancy has been identified in a recent STM experiment using our method. Also, we have calculated the forces between the different defects and an AFM tip, as a complementary tool to identify their respective fingerprint.

Once this methodology has been established, we have considered the adsorption of small inorganic molecules on defective MoS 2 , as a probe for the induced local reactivity. Also, we have calculated conductance and forces between a metallic tip and the adsorbed molecules. As a result, we show that the combination of both calculations (and accordingly measurements, on the experimental side), constitute an accurate way of characterizing these molecules on the defects.

Finally, we have presented very recent results on lateral defective MoS 2 nanoribbons sandwiched between gold electrodes. In these nanojunctions, we consider the same defects as studied previously, and we compare their lateral conductance with what has been obtained previously in STM configuration. We also reveal the most interesting defects for applications, accordingly to their electrical response through the calculation and analysis of the electronic transmission.

This work obviously presents many perspectives. At first, we have established here a simple and complete methodology for characterizing point defects and adsorbed molecules on MoS 2 , as a full support for experimental measurements. Second, the observed modifications of their electronic structure make these materials very promising for applications in nanoelectronics. Indeed, a wide variety of new devices can be designed exploiting the new metallic states emerging in the electronic gap. Also, these new states appear to be very reactive and can be exploited for C. R. Physique -Online first, 25th May 2021 catalysis, or to favor molecular adsorption. In that respect, defective MoS 2 , or as presented in the last section defective MoS 2 nanoribbons offer interesting perspectives for gas sensors, since molecular adsorption modifies the electrical response of the system.

Finally, the last section presented here illustrates also the need to achieve further analysis on the response of the defective MoS 2 nanoribbons. Indeed, the size of the ribbon and its incidence on the electronic properties have to be further explored, in order to limit at most the edge effects. Also, the possibility of gating the nanoribbons has to be considered as well, as the application of a voltage might help in discriminating the different defects (or modifying their reactivity) in order to refine fingerprint. Last but not least, this study can be generalized to other kinds of defects like grain boundaries for example.

Figure 1 .

 1 Figure 1. (a) Top and side view of the atomic structure of a clean single layer of MoS 2 (yellow/blue spheres are S/Mo). The arrows indicate the X and Y directions of the lattice vectors used in the calculation. (b) Calculated electronic DOS for S (black squares) and Mo (red circles) atoms; (c) and (d) show the orbital contributions to the atomic DOS of the S and Mo atoms, respectively. The DOS are separated into directional s +p z +d 2z orbitals (blue uptriangles), in-plane p x +p y (down-triangles) and the sum of the other four d orbitals (yellow hexagons). Reprinted with permission from Ref.[START_REF] González | Theoretical characterisation of point defects on a MoS2 monolayer by scanning tunnelling microscopy[END_REF], copyright IOP 2016.

Figure 2 .

 2 Figure 2. Calculated STM images at 4.5 Å and a bias of (a) -0.1 V and (b) +1.9 V for a clean MoS 2 monolayer. The STM images were graphed using WSxM software [40]. Reprinted with permission from [32], copyright IOP 2016.

Figure 3 .

 3 Figure 3. Calculated STM images at 4.5 Å and a bias of +1.9 V for (a) a Mo vacancy, (b) a Mo vacancy with a substitutional S atom, (c) a Mo vacancy with two substitutional S atoms, (d) a S vacancy, (e) a S vacancy with a substitutional Mo atom, (f) a S divacancy, (g) a S divacancy with a Mo substitutional atom and (h) a S divacancy with two Mo substitutional atoms in a MoS 2 monolayer. The corresponding atomic configurations are superimposed (yellow/blue spheres represent S/Mo atoms).The STM images were graphed using the WSxM software[START_REF] Horcas | WSXM: A software for scanning probe microscopy and a tool for nanotechnology[END_REF]. Reprinted with permission from Ref.[START_REF] González | Theoretical characterisation of point defects on a MoS2 monolayer by scanning tunnelling microscopy[END_REF], copyright IOP 2016.

  C. R. Physique -Online first, 25th May 2021

Figure 4 .

 4 Figure 4. Simulation of AFM experiments: two snapshots representing the interaction of (a) a Cu tip with a Mo vacancy and (b) a Si tip with a S vacancy, both with atomic capture. Force curves of a Cu tip interacting with (c) a S and Mo substituted S vacancy, (d) a S monoand disubstituted Mo vacancy and (e) a Mo mono-and disubstituted S divacancy. In (f-h), same force curves using a Si tip. Reprinted with permission from Ref. [45], copyright ACS 2016.

  C. R. Physique -Online first, 25th May 2021

Figure 5 .

 5 Figure 5. Calculated (a) forces and (b) conductance (in logarithmic scale) for different molecules adsorbed on the defective MoS 2 monolayer: CO (black squares), NO (red circles), CO 2 (green uptriangles), H 2 O (blue down-triangles), O 2 (light-blue rhombus), and N 2 (pink left-triangles). Lateral view of the contact formed between the Cu tip (brown spheres) and the different molecules: (c) N 2 , (d) O 2 , and (e) NO molecules. Inset: The atomic configuration corresponding to both minima of the force in the CO 2 case and the H 2 O molecule. The light-blue, yellow, dark-blue, red, and white spheres correspond to Mo, S, N, O, and H, respectively. Reprinted with permission from Ref. [57], copyright APS 2016.

Figure 6 .

 6 Figure 6. Some optimized configurations for defective MoS 2 nanoribbons sandwiched between gold electrodes: (a) clean MoS 2 , (b) S vacancy, (c) Mo vacancy and (d) S divacany with two Mo substitutional atoms, and an adsorbed water molecule, with an inset focusing on the molecule. The gold, light-blue, yellow, red, and white spheres correspond to Au, Mo, S, O, and H, respectively.

  (a) the clean MoS 2 , (b) the S vacancy, (c) the Mo vacancy and (d) the S divacancy plus two Mo substitutional atoms and a water molecule. Each unit cell has been optimized using Fireball, and the electronic transport has been determined using the same formalism previously used for STM image calculations, one electrode being the tip and the other one plus the defective nanoribbon being the sample in the formalism.

Figure 8 .

 8 Figure 8. Evolution of the electronic transmissions calculated for the different defective MoS 2 nanoribbons presented in Figure 7.

Table 1 .

 1 Formation energy in eV of the different defects on the MoS 2 monolayer: S vacancy (vS), Mo vacancy (vMo), S divacancy (v2S), one or two S atoms occupying the Mo vacancy (vMo+S and vMo+S2) and one or two Mo atoms in a S mono-and divacancy (vS+Mo, v2S+Mo and v2S+Mo2, respectively)

	vS	v2S vMo vS+Mo v2S+Mo v2S+Mo2 vMo+S vMo+S2
	E f (eV) 2.57 5.14 7.22 5.55	7.42	10.75	6.35	9.04

  eV from this state until the first unoccupied state. Regarding S substitutions in Mo vacancies, it is important to stress that the new structure

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Table 2 .

 2 Adsorption energies (eV) at the most stable adsorption sites for each molecule

				E Ads (eV)
	Molecules	CO 2	CO	O 2	H 2 O	NO	N 2	H 2	NO 2
	Pristine	-0.15 -0.09 -0.11 -0.14 -0.15 -0.09 -0.06 -0.28
	vacS	-0.16 -0.14 -3.04 -0.25 -2.88 -0.12 -0.08 -0.28
	vacS+Mo	-0.59 -1.95 -5.12 -1.05 -3.15 -1.54 -1.14 -3.67
	vacMo	-0.17 -0.11 -2.49 -0.16 -0.22 -0.10 -0.06 -1.05
	vacMo+S	-0.14 -0.10 -0.61 -0.19 -0.90 -0.09 -0.06 -0.46
	vacMo+S2 -0.14 -0.10 -0.55 -0.08 -0.12 -0.09 -0.05 -0.34
	vacS2	-0.16 -0.14 -3.11 -0.24 -2.93 -0.11 -0.08 -0.25
	vacS2+Mo -0.41 -1.04 -4.12 -1.28 -3.10 -0.09 -0.52 -4.23
	vacS2+Mo2 -1.19 -1.84 -4.88 -1.63 -4.21 -1.16 -0.78 -3.21
	Reprinted from Ref. [46], copyright RSC 2017.

Table 3 .

 3 Equilibrium distance (Å) at the most stable adsorption sites for each molecule

			∆h (Å)
	Molecules CO 2 CO	O 2 H 2 O NO	N 2	H 2 NO 2
	Pristine	3.32 3.36 2.78 2.37 2.73 3.53 2.75 2.74
	vacS	2.97 2.09 -* 0.85 1.01 2.90 1.90 2.16
	vacS+Mo	2.36 2.00 2.01 2.29 1.82 1.98 -*	-*
	vacMo	3.30 3.00 -* 2.37 0.95 3.53 3.30 1.59
	vacMo+S	3.50 3.25 1.66 2.37 1.92 3.50 2.83 2.31
	vacMo+S2 3.51 1.92 2.52 2.70 2.51 3.00 3.23 2.72
	vacS2	2.95 2.30 -* 1.05 1.13 3.04 2.60 2.85
	vacS2+Mo 2.31 2.20 2.01 2.21 1.82 2.10 1.89 -*
	vacS2+Mo2 2.24 2.05 2.01 2.21 1.81 2.05 1.88 -*

  Evolution of the lateral conductance calculated for different defective MoS 2 nanoribbons: clean, Mo and S vacancy, S vacancy + S divacancy + Mo 2 , S divacancy + Mo 2 + O 2 or CO or NO 2 or NO or H 2 O or H 2 . The dashed green line represents the conductance value of the clean MoS 2 nanoribbon, to facilitate the comparison for the other structures.

C. R. Physique -Online first, 25th May 2021

Figure 7.

C. R. Physique -Online first, 25th May 2021

Acknowledgements

The first author acknowledges financial support from the Community of Madrid through the project NANOMAGCOST, ref P2018/NMT-4321. Also, the authors thankfully acknowledge the computer resources at Calendula and technical support provided by Scayle (projects FI-2020-2-0022 and FI-2020-3-0033).


Daniel Praeg
email: dpraeg@ogs.trieste.it

Riccardo Geletti

Nigel Wardell

Vikram Unnithan

Jean Mascle

Sebastien Migeon

Angelo Camerlenghi

THE MEDITERRANEAN SEA: A NATURAL LABORATORY TO STUDY GAS HYDRATE DYNAMICS?

Keywords: gas hydrate stability, prospectivity, glacial-interglacial climate change

Gas hydrates have been proven by coring at one site in the (eastern) Mediterranean Sea, but their wider extent remains uncertain. Here we present results from investigations of the potential Mediterranean gas hydrate system, suggesting that clathrates occur more widely and have been strongly impacted by glacial-interglacial climate forcing. Modeling of the methane hydrate stability zone (MHSZ) shows it to be present in most of the Mediterranean Sea, albeit in deep waters (>1000 m) due to warm bottom waters (12.5-14°C) and in greater thicknesses (200-500 m) in the geothermally cooler eastern basin. Comparison of the MHSZ with known or possible zones of gas flux to seabed suggests prospective areas for hydrate occurrence, mainly in the eastern basin. One is the Nile fan, where evidence of the first BSR in the Mediterranean Sea (presented sseparately, Praeg et al. this volume) confirms the potential for additional hydrate discoveries. During glacial stages, gas hydrate stability in the Mediterranean increased due to bottom waters up to 4°C cooler; even allowing for sea levels 125 m lower, the modeled glacial-stage MHSZ was up to 25% thicker and 300 m shallower on basin margins. Glacial-to-interglacial transitions thus corresponded to a marked reduction in hydrate stability, with downslope migration of the upper limit of the MHSZ across depths of c. 700-1000 m. A compilation of submarine landslides in the Mediterranean Sea indicates a peak in the age of slide deposits during the last deglaciation and includes abundant headwalls in mid-to upper slope depths (<1200 m), including on the Nile fan. Together these results suggest that the Mediterranean Sea, in particular its gas-rich eastern basin, offers natural laboratory conditions to test the hypothetical linkages between climate-driven changes in gas hydrate stability and slope instabilities over glacial-interglacial timescales.

INTRODUCTION

Changes in gas hydrate stability during glacialinterglacial climate cycles have been hypothesised by various authors to be causally linked to sediment failures on continental margins [START_REF] Mciver | Role of naturally occurring gas hydrates in sediment transport[END_REF][START_REF] Kennett | Methane hydrates in Quaternary climate change: the clathrate gun hypothesis[END_REF][START_REF] Maslin | Linking continental slope failure to climate change: testing the Clathrate Gun Hypothesis[END_REF]. In the Mediterranean Sea, gas hydrate destabilization during lowered sea levels has been proposed as a possible trigger for the emplacement of late-glacial megaturbidites on the floors of the western and eastern basins [START_REF] Rothwell | Low-sealevel emplacement of a very large Late Pleistocene 'megaturbidite' in the western Mediterranean Sea[END_REF][START_REF] Rothwell | Low sea-level stand emplacement of magaturbidites in the western and eastern Mediterranean Sea[END_REF]. To date, however, gas hydrates have been proven to occur at only one location in the eastern basin, in short cores from mud volcanoes [START_REF] Woodside | Shipboard Scientists of the Anaxiprobe expeditions. Shallow gas and gas hydrates in the Anaximander Mountains region, Eastern Mediterranean Sea[END_REF]. Despite evidence that methane hydrates are stable over larger areas, bottom simulating reflections (BSRs) that might indicate their occurrence have not been reported from the Mediterranean Sea [START_REF] Miles | Potential distribution of methane hydrate beneath the European continental margins[END_REF]. This has led to doubts as to whether BSRs have not been recognized, or gas hydrates simply do not occur widely [START_REF] Miles | Potential distribution of methane hydrate beneath the European continental margins[END_REF].

Here we summarise results from investigations by OGS and partners into the gas hydrate system in the Mediterranean Sea, undertaken in the context of recent EC projects (HYDRAMED, HERMES) and an ongoing collaboration (HYDRANIL) that has led to a discovery of a BSR on the Nile fan, presented separately [START_REF] Praeg | Evidence of gas hydrates on the Nile fan[END_REF]. The work is based on modeling of methane hydrate stability, for presentday and glacial-stage conditions, as a guide to geological observations relevant to prospective occurrences and their dynamics. The results point to a wider occurrence of hydrates, particularly in the eastern Mediterranean Sea, and to natural laboratory conditions for testing their relationship to climate forcing and sediment failure.

DATA AND METHODS

The stability zone for methane hydrate in equilibrium with seawater (35‰ NaCl) was calculated using a phase boundary curve obtained from HWHYD [START_REF] Hydrate | [END_REF], which lies between curves from CSMHYD [START_REF] Sloan | Clathrate Hydrates of Natural Gases[END_REF] and that used by [START_REF] Miles | Potential distribution of methane hydrate beneath the European continental margins[END_REF], see Fig. 1. The thickness of the stability zone was calculated, following [START_REF] Miles | Potential distribution of methane hydrate beneath the European continental margins[END_REF][START_REF] Rao | C-program for the calculation of gas hydrate stability zone thickness[END_REF], from the intersection of the curve with 3 parameters (input as 2 minute grids): bathymetry (OGS in-house, C. Zanolla pers. comm.), bottom water temperatures [START_REF] Medar Group | Mediterranean and Black Sea Database of Temperature Salinity and Bio-chemical Parameters[END_REF], and geothermal gradients (compiled for the HYDRAMED project).

METHANE HYDRATE STABILITY Present-Day

The thickness below seabed of the methane hydrate stability zone (MHSZ) is shown in Fig. 2.

The deep Mediterranean Sea is characterized by warm bottom waters (12.5-14°C), meaning that methane hydrates are stable below water depths of 1000-1200 m (Fig. 1), at least twice typical stability limits of 300-500 m in the world ocean [START_REF] Praeg | Evidence of gas hydrates on the Nile fan[END_REF]. Methane hydrates are nonetheless stable throughout the western and eastern Mediterranean basins, each of which reach depths over 3000 m (locally >5000 m in the east). The MHSZ is relatively thin in the western basin (mainly <150 m), due to higher geothermal gradients (typically 50-100°C/km), whereas the geothermally cooler eastern basin (<50°C/km) includes large areas 200-500 m thick; local maxima >500 m (Fig. 2) reflect the sensitivity of the stability zone calculation to individual sites of low (≤10°C/km) geothermal gradient (see Fig. 1).

Glacial Stages

Oxygen isotope (∂ 18 O) variations in cores from the Mediterranean Sea reveal glacial-interglacial cycles of large amplitude, reflecting coevel changes in ice volume (sea level), water temperature and salinity [START_REF] Vergnaud-Grazzini | 18 O changes in foraminifera carbonates during the last 105 years in the Mediterranean Sea[END_REF][START_REF] Vergnaud-Grazzini | Stable isotope "anomalies" in Mediterranean Pleistocene records[END_REF]. Changes in ∂ 18 O values in planktonic and benthic foraminifera since the last glacial maximum (LGM) are interpreted to indicate bottom waters that were saltier and up to 4°C cooler in the eastern basin [START_REF] Vergnaud-Grazzini | Stable isotope "anomalies" in Mediterranean Pleistocene records[END_REF]. This is consistent with estimates based on planktonic assemblages of LGM reductions in winter sea surface temperatures of 4-6°C in the northern Mediterranean, where bottom waters are formed [START_REF] Hayes | Glacial Mediterranean sea surface temperatures based on planktonic foraminiferal assemblages[END_REF]. A 4°C reduction in bottom water temperatures (bwts) has been confirmed by Ca/Mg palaeothermometry of benthic foraminifera in a core from the western basin [START_REF] Cacho | Glacial rapid variability in deepwater temperature and ∂ 18 O from the Western Mediterranean Sea[END_REF]. However, the lowest bwts occurred c. 40 kyr BP, versus LGM bwts up to 3°C lower, as part of fluctuations of several degrees throughout the 50 kya record [START_REF] Cacho | Glacial rapid variability in deepwater temperature and ∂ 18 O from the Western Mediterranean Sea[END_REF].

The MHSZ for glacial stage conditions was modelled by assuming uniformly lower sea level (-125 m) and cooler bottom waters (-4°C). The results (Fig. 3) show that the effects of lowered sea level in increasing hydrate stability were greatly outweighed by the reduction in bottom water temperatures, such that during glacial stages the stability zone was up to 25% thicker and up to 300 m shallower on basin margins (Fig. 4). Thus glacial-to-interglacial transitions throughout the Mediterranean would have corresponded to a marked reduction in hydrate stability, with downslope migration of the upper limit of the MHSZ across depths of c. 700-1000 m (Fig. 4).

HYDRATE PROSPECTIVITY

The dominance of methane in gas hydrate occurrences worldwide means that the MHSZ has been found to provide a useful first approximation to their thicknesses, despite local variations in hydrate stability due to variations in gas composition or pore water salinity [START_REF] Kvenvolden | A primer on the geological occurrence of gas hydrates[END_REF]. Areas of interest for gas hydrate occurrence in the Mediterranean Sea were identified by comparing the MHSZ with known or possible sites of gas flux to seabed. This suggests a wide prospective occurrence, particularly in the eastern Mediterranean (Fig. 2).

In the western Mediterranean, gas hydrate prospectivity is lower due to the paucity of evidence for deep-water gas flux into a relatively thin (<150 m) MHSZ. Mud volcanoes have been proven only in the Alboran Sea, where evidence of episodic activity since the Pliocene [START_REF] Talukder | Pliocene to Recent mud diapirism and related mud volcanoes in the Alboran Sea (Western M e d i t e r r a n e a n )[END_REF] implies a long history of gas flux to seabed. Two other areas of possible gas seepage are postulated. One is the Algerian margin, a convergent tectonic setting affording pathways for upward fluid migration and an area of current interest for deep-water hydrocarbon exploration [START_REF] Cope | Algerian licensing round may offer opportunity for exploration plays in deep offshore frontier[END_REF]. Another is the Rhone fan, a Plio-Quaternary depocentre up to 2 km thick [START_REF] Droz | Quaternary turbidite systems on the northern margins of the Balearic Basin (Western Mediterranean): a synthesis[END_REF] that could consitute a source of biogenic gas. In all three areas (Fig. 2), the base of the MHSZ is within 150 m of seabed, complicating the identification of any BSRs.

Gas hydrate prospectivity is higher in the eastern Mediterranean basin (Fig. 2), where the MHSZ is thicker and evidence of gas flux to seabed is widespread. The eastern Mediterranean contains one of the world's highest abundances of mud volcanoes [START_REF] Kopf | Significance of mud volcanism[END_REF], most of which lie along the accretionary system formed by subduction of the African beneath the European plate [START_REF] Kopf | Significance of mud volcanism[END_REF][START_REF] Huguen | Morphology of a pre-collisional, saltbearing, accretionary complex: the Mediterranean Ridge (Eastern Mediterranean)[END_REF]. Gas hydrates have been cored in mud volcanoes in the eastern part of the accretionary system in the Anaximander Mountains [START_REF] Woodside | Shipboard Scientists of the Anaxiprobe expeditions. Shallow gas and gas hydrates in the Anaximander Mountains region, Eastern Mediterranean Sea[END_REF], an area where the stability zone thins to <200 m (Fig. 2). Gas hydrates have not been proven in other mud volcanoes of the accretionary system, despite a false report from the Milano mud volcano based on pore water profiles acquired during ODP leg 160 [START_REF] Lange | Pore-water indications for the occurrence of gas hydrates in Eastern Mediterranean mud dome structures[END_REF][START_REF] Dählmann | Fluid-sediment interactions at Eastern Mediterranean mudvolcanoes: a stable isotope study from ODP Leg 160[END_REF]. However, these and other investigations of mud volcanoes within the accretionary system, from the Calabrian Arc to Cyprus, have found geological and biological evidence of ongoing seepage of gas-rich fluids and free gas, mainly biogenic methane [START_REF] Charlou | Evidence of methane venting and geochemistry of brines on mud volcanoes of the eastern Mediterranean Sea[END_REF][START_REF] Foucher | Structure and drivers of cold seep ecosystems[END_REF]. These findings have been noted to suggest that gas hydrate occurrences may be widespread along the accretionary system [START_REF] Charlou | Evidence of methane venting and geochemistry of brines on mud volcanoes of the eastern Mediterranean Sea[END_REF].

Areas of interest are also present to the south along the passive margins of northern Africa (Fig. 2), from Libya to the Levant, which are currently a focus for oil and gas exploration [START_REF] Belopolsky | New Plays in the Eastern Mediterranean[END_REF]. Of particular interest is the Nile deep-sea fan, a Plio-Quaternary depocentre up to 4 km thick that is rich in seabed features of fluid seepage (e.g. mud volcanoes, pockmarks, carbonate crusts) [START_REF] Loncke | Fanil Scientific Parties. Mud volcanoes, gas chimneys, pockmarks and mounds in the Nile deep-sea fan (eastern Mediterranean); geophysical evidences[END_REF][START_REF] Dupré | Widespread active seepage activity on the Nile Deep Sea Fan (offshore Egypt) revealed by high-definition geophysical imagery[END_REF]. Several of these features have been shown to emit gas and gas-rich fluids, including thermogenic methane and higher hydrocarbons [START_REF] Mastalerz | Active venting at the Isismud volcano, offshore Egypt: origin and migration of h y d r o c a r b o n s . C h e m i c a l[END_REF][START_REF] Bayon | Multi-disciplinary investigation of fluid seepage on an unstable margin: the case of the Central Nile deep sea fan[END_REF]. In the central Nile fan, an area of pockmarks and carbonate crusts, investigations by OGS and partners have yielded evidence of a BSR, in water depths of c. 2000-2500 m, consistent with a gas hydrate occurrence zone up to 250 m thick [START_REF] Praeg | Evidence of gas hydrates on the Nile fan[END_REF]. This discovery serves to confirm the potential for additional discoveries of gas hydrates in the Mediterranean Sea, particularly its eastern basin.

GLACIAL-INTERGLACIAL DRIVERS

Glacial-interglacial changes in sea level (pressure) have an instantaneous and pervasive effect on gas hydrate stability, but can be countered by even small (<1°C) temperature changes, moreso at greater depths as the phase boundary curve steepens (Fig. 1). Changes in bottom water temperatures must diffuse to the base of the stability zone, over timescales typically up to 10 3 years [START_REF] Kvenvolden | A primer on the geological occurrence of gas hydrates[END_REF], but that decrease as the stability zone thins towards its upper limit, the so-called critical wedge [START_REF] Mciver | Role of naturally occurring gas hydrates in sediment transport[END_REF]. The world ocean has experienced an increase in bwts of between 2-5°C since the last glaciation [START_REF] Adkins | T h e salinity, temperature and ∂ 18 O of the glacial deep ocean[END_REF] and a number of studies have shown they were capable of destabilising gas hydrates despite rising sea levels [START_REF] Kennett | Carbon isotopic evidence for methane hydrate instability during Quaternary interstadials[END_REF][START_REF] Bangs | Upward shifts in the southern Hydrate Ridge gas hydrate stability zone following postglacial warming, offshore Oregon[END_REF][START_REF] Mienert | Ocean warming and gas hydrate stability on the mid-Norwegian margin at the Storegga Slide[END_REF]. The impact is less at greater depths, where bottom waters tend to be with a few degrees of freezing, but increases to a maximum impact at upper slope depths, i.e. within the critical wedge [START_REF] Mienert | Ocean warming and gas hydrate stability on the mid-Norwegian margin at the Storegga Slide[END_REF]. A different impact is recognized in enclosed basins such as the Black Sea, where the entire deep-water (>700 m) gas hydrate stability zone is argued to be undergoing contraction following marine flooding 7.1 kyr BP that increased bottom water temperatures by between 2-5.5°C [START_REF] Poort | D i d postglacial catastrophic flooding trigger massive changes in the Black Sea gas hydrate reservoir?[END_REF].

In the Mediterranean Sea, the deglacial increase in bottom water temperatures took place >15 kyr ago and so should have largely diffused through the gas hydrate stability zone [see 34 -36]. Thus the entire zone of hydrate stability will have been modified by the large increase in bwts, inferred above to have driven basin-wide reductions in thickness of up to 25% and downslope migration of the critical wedge across depths of c. 700-1000 m (Fig. 4). These findings provide a new perspective on the possible causes of slope instabilities in the Mediterranean Sea, which have previously been considered only in relation to reductions in gas hydrate stability due to falling (or lowered) sea levels [START_REF] Rothwell | Low-sealevel emplacement of a very large Late Pleistocene 'megaturbidite' in the western Mediterranean Sea[END_REF][START_REF] Rothwell | Low sea-level stand emplacement of magaturbidites in the western and eastern Mediterranean Sea[END_REF][START_REF] Garziglia | Giant mass-transport deposits on the Rosetta province continental slope (NW Nile Deep-sea fan, Egyptian margin): characteristics, distribution, and potential causal processes[END_REF].

A recent compilation of submarine landslides in the Mediterranean Sea [START_REF] Camerlenghi | A database on submarine landslides of the Mediterranean Sea[END_REF] shows a peak in the age of failures between c. 10-20 ka BP (Fig. 5), following the last glacial maximum and coincident with the deglacial rise in sea levels. Most slide headwalls lie in depths less than 1200 m on the mid-to upper continental slope (Fig. 5). The longest record of sediment failure comes from the Nile fan, where 7 mass transport deposits (MTDs) date back over 100 ka to the last interglacial [START_REF] Garziglia | Giant mass-transport deposits on the Rosetta province continental slope (NW Nile Deep-sea fan, Egyptian margin): characteristics, distribution, and potential causal processes[END_REF].

Only one of these MTDs, dated to isotopic stage 5d, coincided with falling sea levels that could have driven gas hydrate destabilization [START_REF] Garziglia | Giant mass-transport deposits on the Rosetta province continental slope (NW Nile Deep-sea fan, Egyptian margin): characteristics, distribution, and potential causal processes[END_REF].

Another is of deglacial age, forming part of the peak in Fig. 5. Interestingly, subsequent work has dated one of the Nile fan MTDs to c. 35-40 kyr BP [START_REF] Rouillard | Modèles architectural et lithologique des dépôts quaternaires du système de Rosetta (Delta Profond du Nil, Méditerranée orientale) : implication pour un analogue actuel de réservoirs pétroliers[END_REF], just after the 40 kyr bwt minimum recorded by Ca-Mg palaeothermometry in the western Med, argued to be a regional climate signal that also affected the eastern Mediterranean [START_REF] Cacho | Glacial rapid variability in deepwater temperature and ∂ 18 O from the Western Mediterranean Sea[END_REF].

Unfortunately no independent records of bottom water temperatures are available for the eastern Mediterranean basin, which may have experienced palaeoceanographic conditions resulting in differing thermohaline circulation histories.

Several other factors may trigger submarine landslides, e.g sediment supply, fluid flow, seismicity [START_REF] Garziglia | Giant mass-transport deposits on the Rosetta province continental slope (NW Nile Deep-sea fan, Egyptian margin): characteristics, distribution, and potential causal processes[END_REF]. Nonetheless, evidence that the Mediterranean Sea has experienced large glacialinterglacial changes in bottom water temperatures suggest that, where they occur, destabilization of gas hydrates represents a viable triggering mechanism for sediment failure. This mechanism could account for the observed deglacial peak in submarine landslides (Fig. 5), including on the Nile fan where gas hydrates are inferred to be present [START_REF] Praeg | Evidence of gas hydrates on the Nile fan[END_REF]. Inversely, additional investigations of the Mediterranean Sea, in particular its eastern basin, offer the opportunity to test the relationship of climate-driven changes in hydrate stability of high amplitude against long stratigraphic records of sediment failure. To take advantage of this opportunity requires an independent record of bottom water temperatures through time in the eastern basin, as well as additional information both on the ages and sources of failures.

CONCLUSIONS

The preceding shows that methane hydrates are stable throughout the Mediterranean deep water (>1000 m) basins and potentially occur more widely in the gas-rich eastern basin; this potential is confirmed by the identification of a BSR on the Nile fan [START_REF] Praeg | Evidence of gas hydrates on the Nile fan[END_REF]. In addition, hydrate stability is shown to have significantly decreased since the last glaciation due to an increase in bottom water temperatures by up to 4°C, which could account for a deglacial peak in the ages of submarine landslides. These results invite further investigations for which the Mediterranean, in particular its eastern basin, appears to offer natural laboratory conditions to test the linkages between high-amplitude climate-drivers, changes in gas hydrate stability and slope instabilities over glacial-interglacial timescales.

Figure 1 .

 1 Figure 1. Phase boundary curve for methane hydrate in equilibrium with seawater from HWHYD [9] compared to two others [7,10]; superimposed are typical parameters for the Mediterranean Sea.

Figure 2 .

 2 Figure 2. Modelled methane hydrate stability zone for present-day conditions, with areas of interest for hydrate occurrence; orange triangles indicate the general locations of known seabed seeps (various sources).

Figure 3 .

 3 Figure 3. Modelled methane hydrate stability zone for glacial stage conditions.

Figure 4 .

 4 Figure 4. Transect of modelled methane hydrate stability zones in the eastern Mediterranean.

Figure 5 .

 5 Figure 5. Ages and headwall depths of submarine landslides in the Mediterranean Sea (from Camerlenghi et al. 2010).

ACKNOWLEDGEMENTS

This work builds on the EC HYDRAMED project, funded by a Marie Curie Intra-European Individual Fellowship held by D. Praeg at OGS, within the European Community 6th Framework Programme (contract MEIF-CT-2003-501814, 2004-2006).