Lukasz Wolski
email: wolski.lukasz@amu.edu.pl

Oleg I Lebedev

Colin P Harmer

Kirill Kovnir

Hanen Abdelli

Tomasz Grzyb

Marco Daturi

Mohamad El-Roz
email: mohamad.elroz@ensicaen.fr

Adam Mickiewicz

Unravelling the origin of photocatalytic deactivation in CeO2/Nb2O5 heterostructure systems -Insight into the role of cerium species

Keywords: niobium pentoxide, cerium dioxide, methanol photooxidation, recombination of charge carriers

Introduction

Cerium dioxide is one of the most intensively studied model heterogeneous catalysts.

Hitherto, it has been established that ceria can be successfully used not only as a support for various active phases but it can also be involved as a promising active component for various reactions [START_REF] Montini | Fundamentals and Catalytic Applications of CeO2-Based Materials[END_REF] . Recently, cerium dioxide has been thoroughly studied for applications in advanced oxidation processes, e.g. photocatalytic oxidation [START_REF] Bakkiyaraj | Solution Combustion Synthesis and Physico-Chemical Properties of Ultrafine CeO2 Nanoparticles and Their Photocatalytic Activity[END_REF][START_REF] Cui | Enhancement of the Visible-Light Photocatalytic Activity of CeO2 by Chemisorbed Oxygen in the Selective Oxidation of Benzyl Alcohol[END_REF][START_REF] Majumder | Facet-Dependent Photodegradation of Methylene Blue Using Pristine CeO2 Nanostructures[END_REF] or Fenton-like reactions [START_REF] Hamoud | Removal of Binary Dyes Mixtures with Opposite and Similar Charges by Adsorption, Coagulation/Flocculation and Catalytic Oxidation in the Presence of CeO2/H2O2 Fenton-like System[END_REF][START_REF] Cai | Enhanced Catalytic Degradation of AO7 in the CeO2-H2O2 system with Fe 3+ doping[END_REF][START_REF] Chen | CeO2/H2O2 system Catalytic Oxidation Mechanism Study via a Kinetics Investigation to the Degradation of Acid Orange 7[END_REF] . Many authors have reported that doping of semiconducting metal oxides with ceria is an efficient method to improve the photocatalytic performance of parent oxides. For instance, Zhu et al. [START_REF] Zhu | Hierarchical ZnO Decorated with CeO2 Nanoparticles as the Direct Z-Scheme Heterojunction for Enhanced Photocatalytic Activity[END_REF] have documented that CeO2/ZnO composites displayed highly enhanced photocatalytic activity in Rhodamine B (RhB) degradation compared to pristine ZnO and CeO2. The increase in activity of the CeO2/ZnO heterostructures was attributed by the authors to formation of Z-scheme heterojunction, which improved the separation of photo-generated charge carriers. Improved efficiency of charge carriers separation resulting from formation of heterojunctions has also been reported for CeO2/TiO2 systems in photooxidation of toluene [START_REF] Muñoz-Batista | Role of Interface Contact in CeO2-TiO2 Photocatalytic Composite Materials[END_REF] and photodegradation of phenazopyridine drugs [START_REF] Eskandarloo | TiO2/CeO2 Hybrid Photocatalyst with Enhanced Photocatalytic Activity: Optimization of Synthesis Variables[END_REF] . However, the above-mentioned paradigm concerning the positive role ceria doping plays in improving the photocatalytic activity of various semiconducting metal oxides has been recently rebutted by Morlando et al. [START_REF] Morlando | Development of CeO2 Nanodot Encrusted TiO2 Nanoparticles with Reduced Photocatalytic Activity and Increased Biocompatibility towards a Human Keratinocyte Cell Line[END_REF] . The authors found that deposition of CeO2 nanodots on the surface of TiO2 led to significant decrease in photocatalytic activity of the as-formed composite materials. The authors claimed that the decrease in activity of CeO2/TiO2 nanocomposites may have resulted from scavenging of reactive oxygen species by cerium species, increased recombination of photo-excited charge carriers caused by ceria doping and/or UV shielding effects from ceria loading on the surface of TiO2. Deactivation of photocatalysts after ceria doping was also observed for CeO2/ZnO heterostructures [START_REF] Mueen | ZnO/CeO2 Nanocomposite with Low Photocatalytic Activity as Efficient UV Filters[END_REF] .

According to the authors, deactivation of this catalytic system arose from the presence of ultrafine CeO2 nanoparticles with existing surface defects which could impart some form of reactive oxygen species scavenging property. However, no evidence supporting the abovementioned hypotheses, explaining deactivation of TiO2 or ZnO photocatalysts after loading of ceria species, has been provided.

Besides ZnO and TiO2, niobium pentoxide (Nb2O5) is another semiconductor which has been successfully used in photocatalytic reactions [START_REF] Su | Nb2O5 -Based Photocatalysts[END_REF][START_REF] Riente | Application of Metal Oxide Semiconductors in Light-Driven Organic Transformations[END_REF][START_REF] Tamai | Synthesis of Niobium Oxide Nanoparticles with Plate Morphology Utilizing Solvothermal Reaction and Their Performances for Selective Photooxidation[END_REF][START_REF] Kulkarni | Nanostructured N-Doped Orthorhombic Nb2O5 as an Efficient Stable Photocatalyst for Hydrogen Generation under Visible Light[END_REF][START_REF] Zhao | Shape-Dependent Acidity and Photocatalytic Activity of Nb2O5 Nanocrystals with an Active TT (001) Surface[END_REF] . Niobia is known for its high Brønsted acidity which can play an important role in controlling the selectivity of various processes [START_REF] Riente | Application of Metal Oxide Semiconductors in Light-Driven Organic Transformations[END_REF][START_REF] Nowak | Niobium Compounds: Preparation, Characterization, and Application in Heterogeneous Catalysis[END_REF][START_REF] Ftouni | TiO2/Zeolite Bifunctional (Photo)Catalysts for a Selective Conversion of Methanol to Dimethoxymethane: On the Role of Brønsted Acidity[END_REF] . Previous reports show the photocatalytic activity of Nb2O5 can also be improved by forming heterojunctions with other semiconductors (e.g. Nb2O5/TiO2 20,21 , Nb2O5/ZnO 22 , Nb2O5/Bi2WO6 23 , NiO/Nb2O5 24 and Nb2O5/g-C3N4 [START_REF] Hong | Efficient and Stable Nb2O5 Modified g-C3N4 Photocatalyst for Removal of Antibiotic Pollutant[END_REF] ). However, to the best of our knowledge, there are no fundamental studies evaluating the influence of ceria doping on the photocatalytic activity of niobium pentoxide. In view of the recent results, reporting the ambiguous negative/positive role of ceria dopant in CeO2/ZnO and CeO2/TiO2 heterostructures, a fundamental evaluation of the cerium species' role in controlling the activity of niobia-based photocatalysts is crucial for rational development of ceria-containing photocatalysts.

The present study establishes the influence of ceria doping on the structure, texture, and photocatalytic performance of niobium pentoxide. Ceria species were loaded on niobia surface by wet impregnation. Photocatalytic activity of parent metal oxides (i.e. Nb2O5 and CeO2) and as-prepared CeO2/Nb2O5 heterostructures with different ceria loading was tested in methanol oxidation, a well-known model reaction which allows to determine relationship between properties of materials and their catalytic performance. Operando-IR techniques provided insight into the mechanism of the photocatalytic process across CeO2/Nb2O5 heterostructures while elucidating the role individual components of each heterostructure play in methanol photooxidation [START_REF] Tatibouet | Methanol Oxidation as a Catalytic Surface Probe[END_REF][START_REF] Kähler | Methanol Oxidation as Probe Reaction for Active Sites in Au/ZnO and Au/TiO2 Catalysts[END_REF][START_REF] Crampton | Methanol Photo-Oxidation on Rutile TiO2 Nanowires: Probing Reaction Pathways on Complex Materials[END_REF] .

Experimental

Synthesis of Nb2O5

Niobium pentoxide was synthesized using the hydrothermal procedure described by Murayama et al. [START_REF] Murayama | Hydrothermal Synthesis of Octahedra-Based Layered Niobium Oxide and Its Catalytic Activity as a Solid Acid[END_REF] . In a typical synthesis route, ammonium niobate(V) oxalate hydrate (Sigma-Aldrich, C4H4NNbO9 x H2O, 99.99%) (9.0894 g, 30 mmol) was dissolved in 200 mL of deionized water. Following 1 h of vigorous stirring, the pellucid solution was sealed in a teflonlined stainless-steel autoclave and heated for 24 h at 175 °C. The solid formed during hydrothermal treatment was then separated by filtration, washed with deionized water, dried at room temperature and calcined for 2 h at 400 °C (temperature ramp: 1.6 °C/min). The asprepared material was denoted as Nb2O5.

Loading of ceria species on the niobia support

Ceria species were loaded on the surface of Nb2O5 via a facile wet impregnation method.

In a typical synthesis, 6 g of as-prepared Nb2O5 was dispersed in 10 mL of deionized water.

Meanwhile, cerium(III) nitrate hexahydrate (Sigma-Aldrich, 99.99%) was dissolved in 35 mL of deionized water (the amount of cerium source was adjusted to obtain 1.0, 5.0 or 10.0 wt.% of Ce on the niobia support). Next, the solution of cerium(III) nitrate hexahydrate was stirred into the mixture containing niobium pentoxide dispersed in water. Following 1 h of agitation at room temperature, the mixture was transferred to a round bottom flask and sonicated for 10 min. In the next step, water was evaporated from the mixture using a rotary evaporator and the as-obtained powder was dried in a furnace at 80 °C for 12 h. Finally, the dry powder was calcined at 400 °C for 2 h (temperature ramp: 1.6 °C/min). The as-prepared ceria-doped catalysts containing 1.0, 5.0 or 10.0 wt.% of Ce were labelled as Ce1/Nb2O5, Ce5/Nb2O5, and Ce10/Nb2O5, respectively. Mechanical CeO2/Nb2O5 mixtures were prepared using Nb2O5 and commercial CeO2.

For this purpose, appropriate amounts of metal oxides were mixed with small amount of deionized water and then crushed in agate mortar to get homogeneous mixture. Next, the asobtained mechanical mixtures of metal oxides were dried overnight at 70 °C to obtain dry powders. The as-prepared materials were used as reference samples.

Characterization of catalysts

The catalysts were characterized with the use of inductively coupled plasma-optical emission spectrometry (ICP-OES), nitrogen physisorption, powder X-ray diffraction (PXRD), high resolution transmission electron microscopy (HR TEM), UV-visible spectroscopy (UVvis), X-ray photoelectron spectroscopy (XPS), and photoluminescence measurements (PL).

Powder X-ray diffraction patterns were collected on a benchtop Rigaku Miniflex 600 with Cu Kα radiation (λ= 1.5406 Å) and Ni-Kβ filter. Peak locations of each sample were refined against a Si internal standard (Si 640d, Fd-3m, a = 5.43123 Å) via Rietveld refinement in GSAS-II [START_REF] Toby | GSAS-II: The Genesis of a Modern Open-Source All Purpose Crystallography Software Package[END_REF] . Rietveld refinement was initiated by determining sample displacement from the Si internal standard. Then size and preferred orientation were refined to best fit each sample before refining unit cell parameters.

Transmission electron microscopy (TEM) was performed using JEM ARM200F cold FEG probe and image aberration corrected microscope, operated at 200 kV and equipped with large angle CENTURIO EDX detector, Orius Gatan CCD camera and Quantum GIF. The TEM samples were prepared in conventional way -depositing solution of the material in ethanol on a carbon holey Cu grid.

Diffuse reflectance UV-vis spectra (DR UV-vis) were recorded on a Varian Cary 300 Scan spectrophotometer equipped with a diffuse reflectance accessory. Spectra were recorded at room temperature from 200 to 800 nm using Spectralon as a reference material.

Photoluminescence properties were studied at room temperature using a PIXIS:256E Digital CCD Camera equipped with an SP-2156 Imaging Spectrograph (Princeton Instruments) and Opolette 355LD UVDM tuneable laser as the excitation source (with repetition rate 20 Hz; 0.5 mJ pulse energy at 250 nm). All spectra were corrected for spectral response of the equipment. The beam size and laser powers were determined by a 10A-PPS power meter (Ophir Photonics).

The N2 adsorption-desorption isotherms were obtained at -196 °C using a Micromeritics ASAP 2020 Physisorption Analyzer. Before the measurements, samples were degassed at 120 °C for 10 h. The surface area of the materials obtained was estimated by the Brunauer-Emmett-Teller (BET) method.

X-ray photoelectron spectroscopy (XPS) was performed using an ultra-high vacuum photoelectron spectrometer based on Phoibos150 NAP analyzer (Specs, Germany). The analysis chamber was operated under vacuum with a pressure close to 5 × 10 -9 mbar and the sample was irradiated with a monochromatic Al Kα (1486.6 eV) radiation. Any charging that occurred during the measurements (due to incomplete neutralization of ejected surface electrons) was accounted for by rigidly shifting the entire spectrum by a distance needed to set the binding energy of the C1s assigned to adventitious carbon to the assumed value of 284.8 eV.

Photocatalytic tests

The photocatalysts were pressed into self-supported wafers (Ø =16 mm, m ≈ 11.7 mg/cm 2 ) of about 65 ± 2 μm in thickness. The outlet gas phase evolution was followed by both IR spectroscopy and mass spectrometry. FT-IR spectra of the outlet gas phase and of the samples were collected with a Nicolet 5700 FT-IR spectrometer (64 scans/spectrum) equipped with an MCT detector. The operando-IR system was connected to a flow set-up [START_REF] Wuttke | Discovering the Active Sites for C3 Separation in MIL-100(Fe) by Using Operando IR Spectroscopy[END_REF] . Gases were introduced into the lines by mass flow controllers. The system allows the two gas mixtures, the so-called "activation" and "reaction" flows, to be prepared and sent independently to the reactor cell. The "Sandwich" type reactor-cell used in this study is described in reference [START_REF] El-Roz | An Operando-IR Study of Photocatalytic Reaction of Methanol on New *BEA Supported TiO2 Catalyst[END_REF] . It was made of a stainless-steel cylinder that carries a toroidal sample holder in its center, where the catalyst self-supporting wafer was placed. Tightness was obtained by O-rings, and the dead volume (typically defined as the residual space between each sample face and the windows) was reduced to about 0.4 mL by filling the empty space with KBr windows placed on each side of the sample holder. The sample analysis was made possible without the superposition of the gas phase signal and fluid dynamics. Gases were introduced to the sample and evacuated by two 1/8-inch OD pipes connected to the opposite sides of the sample holder. In this study, UV irradiation was carried using a UV light guide (A10014-50-0110) mounted at the entrance to the IR cell and connected to a polychromatic light of Xe-Hg lamp (LC8 spot light Hamamatsu, L10852, 200 W) equipped with a filter to enable monochromatic UV irradiation (λ = 365 nm).

More details on the operando-IR system for photocatalysis can be found in references [START_REF] El-Roz | An Operando-IR Study of Photocatalytic Reaction of Methanol on New *BEA Supported TiO2 Catalyst[END_REF] and 33 .

The employed configuration allowed a low partial pressure of methanol to be achieved using a saturator at controlled temperature. The gas mixture composition was fixed then at 0.12 vol. % methanol and 20 vol. % O2 in Ar and the total flow was adjusted to 20 cm 3 /min. Outlet gasses were characterized by a Pfeiffer Omnistar mass spectrometer. FT-IR spectra of the gas phase were collected using a gas microcell. The conversions were calculated at the steady state.

Results and discussion

Photocatalytic tests

Photocatalytic activity of materials was tested via methanol oxidation in gas phase. The results are shown in Fig. 1a. The highest methanol conversion of 24.6 % was observed for undoped Nb2O5. Commercial CeO2 was significantly less active than undoped niobium pentoxide and its activity at 5.3 %. As can be seen from Fig. 1a, all ceria-doped samples exhibited significantly lower activity than unmodified Nb2O5. In the case of Ce1/Nb2O5 activity was reduced by more than 50 % compared to pristine niobia (24.6 % vs. 11.9 % of methanol conversion for Nb2O5 and Ce1/Nb2O5, respectively). More pronounced decrease in the activity of the composite catalysts was observed for Ce5/Nb2O5. Interestingly, for Ce10/Nb2O5 photocatalytic activity of the heterostructure was totally quenched. There were no products formed during the methanol photooxidation over this catalyst. To gain deeper insight into the quenching of catalysts' activity after loading of ceria on niobia we performed additional measurements with mechanical mixtures of metal oxides as reference samples. We found that activity of these mechanical mixtures of metal oxides containing 1 wt.% and 10 wt.% of Ce was only slightly lower than that observed for unmodified Nb2O5 (see Fig. 1b). Interestingly, the activity of mechanical mixtures of CeO2 and Nb2O5 oxides was not quenched even at very high concentration of CeO2 in the composite material (Nb2O5:CeO2 weight ratio of 1:1). As can be seen from Fig. 1, such mixture of metal oxides was still slightly more active than commercial CeO2. To shed light on the role of cerium species in deactivation of ceria-doped samples, prepared by wet impregnation, we compared the activity of these materials with the activity of mechanical mixtures of metal oxides and theoretical activity of the composite materials expected at given concentration of CeO2 and Nb2O5 in the heterostructures (theoretical methanol conversion was estimated by summing up the activity of given amount of Nb2O5 and commercial CeO2 in the composite). According to our results, the activity of mechanical mixtures of metal oxides was always lower than the expected theoretical values, but was still significantly higher than the activity of samples prepared by wet impregnation (see Fig. 1b). This observation led us to conclude that deactivation of the composite catalysts prepared by wet impregnation should be somehow related to the unique properties of these materials and their interaction.

To further probe the role of the ceria dopant in the photocatalytic process, operando-IR studies have been performed. According to literature [START_REF] El-Roz | On the Mechanism of Methanol Photooxidation to Methylformate and Carbon Dioxide on TiO2: An Operando-FTIR Study[END_REF] , the first step of methanol photooxidation is the adsorption of methyl alcohol on the catalyst surface and consequently the formation of surface methoxy species. Operando-IR studies show that exposure of all catalysts to the gas feed led to immediate disappearance of IR bands typical of surface hydroxyl groups of niobia and ceria (e.g. IR bands at ca. 3662 cm -1 characteristic of bridged OH groups in the fluorite structure of ceria [START_REF] Binet | IR Study of Polycrystalline Ceria Properties in Oxidised and Reduced States[END_REF][START_REF] Daturi | Study of Bulk and Surface Reduction by Hydrogen of CexZr1-xO2 Mixed Oxides Followed by FTIR Spectroscopy and Magnetic Balance[END_REF] ) and appearance of several new IR bands typical of adsorbed methanol molecules (e.g. IR bands in the range from 2750 cm -1 to 3000 cm -1 [START_REF] El-Roz | New Operando IR Technique to Study the Photocatalytic Activity and Selectivity of TiO2 nanotubes in Air Purification: Influence of Temperature, UV Intensity, and VOC Concentration[END_REF][START_REF] Kähler | Probing the Reactivity of ZnO and Au/ZnO Nanoparticles by Methanol Adsorption: A TPD and DRIFTS Study[END_REF] ; see Fig. S1, Supporting Information). Detailed analysis of the adsorbed methoxy species, in the range of wavelengths shown in Fig. S1, is problematic since the typical C-H vibration bands overlap with the characteristic O-H vibration bands of adsorbed water. Thus, detailed analysis of adsorbed species on catalysts surfaces was performed on the basis of FTIR spectra in the range of wavenumbers where characteristic vibrations of adsorbed methoxy groups are not overlapped with other vibrational bands (i.e. at 1200-1000 cm -1 38 ). Fig. 2 shows surface FTIR spectra of catalysts at the equilibrium state during methanol adsorption under dark conditions.

In the case of ceria is easy to identify the bands due to linearly (1112 cm -1 ) and two-fold (1057 cm -1 ) coordinated methoxys on Ce 4+ 38 . The components at 1039 cm -1 is assigned to bridged species on Ce 4+ cations in the proximity of an oxygen vacancy [START_REF] Daturi | Surface Investigation on CexZr1-xO2 Compounds[END_REF] . The other bands observed at higher wavenumbers are due to carbonate impurities belonging to ceria exposure to air [START_REF] Daturi | Surface Investigation on CexZr1-xO2 Compounds[END_REF] and to residual oxalates on the surface of niobia. Analysis of IR spectra recorded for niobia-based samples allowed discrimination of three components at ca. 1158, 1125 and 1105 cm -1 . The first component at ca. 1158 cm -1 is characteristic of ρ(CH3) rocking mode of methoxy species 39 , while the latter two IR bands are typical of ν(OC) vibration modes of linearly (1125 cm -1 ) and may be two-fold (or another linear species coordinated on different exposed crystal planes -at 1105 cm -1 ) coordinated methoxy species on niobia [START_REF] Moulin | How to Determine IR Molar Absorption Coefficients of Co-Adsorbed Species? Application to Methanol Adsorption for Quantification of MgO Basic Sites[END_REF] . We found no significant differences in the forms and concentration of methoxy species on the surface of unmodified Nb2O5 and ceriadoped samples prepared by wet impregnation. Even at relatively high loading of cerium species (10 wt.%), no noticeable IR bands typical of aforementioned methoxy species bonded to ceria surface were found. In view of these observations, we concluded that quenching of niobia activity through loading of ceria by wet impregnation cannot be attributed to covering of niobia surface by cerium species and/or hindering of niobia ability to adsorb methanol molecules. The second step in photocatalytic oxidation of methanol is oxidation of adsorbed methoxy species to formaldehyde [START_REF] El-Roz | On the Mechanism of Methanol Photooxidation to Methylformate and Carbon Dioxide on TiO2: An Operando-FTIR Study[END_REF] . The as-formed formaldehyde can then be desorbed from catalyst surface or further transformed into other products such as methyl formate, formic acid, or carbon dioxide. According to literature, oxidation of formaldehyde to other products leads to appearance of some reaction intermediates, such as adsorbed formate species, characterized by the vibrational bands at ca. 1565, 1371 and 1356 cm -1 for commercial CeO2 and ca. 1577, 1385 and 1365 cm -1 for niobia-based photocatalysts [START_REF] El-Roz | An Operando-IR Study of Photocatalytic Reaction of Methanol on New *BEA Supported TiO2 Catalyst[END_REF][START_REF] El-Roz | On the Mechanism of Methanol Photooxidation to Methylformate and Carbon Dioxide on TiO2: An Operando-FTIR Study[END_REF] . As can be seen from sample FTIR spectra of undoped Nb2O5 and commercial CeO2 shown in Fig. 3a, typical IR bands for these reaction intermediates showed up immediately after irradiation of the catalysts with UV light and continue to increase intensity upon irradiation. The increase in intensity of typical IR bands of adsorbed formate species was associated with a decrease in intensity of characteristic IR bands of adsorbed methanol molecules (IR bands in the range 1200-1000 cm -1 ). This observation led us to conclude that methanol is efficiently oxidized on the surface of these two unmodified metal oxides. Even, on ceria the oxidation proceeds until CO2, as witnessed by the formation of bidentate carbonates on the surface of the samples (bands at 1594 and 1304 cm -1 ) [START_REF] Daturi | Surface Investigation on CexZr1-xO2 Compounds[END_REF] . However, a different trend was observed for ceria-doped samples prepared by wet impregnation. As can be seen from Fig. 3b, the changes in intensity of IR bands characteristic of adsorbed formate species was significantly suppressed for the Ce1/Nb2O5 and Ce5/Nb2O5 catalysts. In the case of reaction with the use of Ce10/Nb2O5, almost no changes in intensity of IR bands typical of adsorbed formate species were found. Also, no changes were observed for this catalyst in the range of wavenumbers characteristic of adsorbed methoxy species (see Fig. 3a). It is worth noting that for all niobia-based samples methanol conversion was found to be proportional to the intensity of IR bands characteristic of adsorbed formate species (see Fig. 3c). Thus, IR experimental data indicated that a decrease in activity of heterostructures prepared by wet impregnation resulted from their reduced ability to oxidize methanol molecules adsorbed on niobia surface. (c)

Characterization of catalysts

To understand the origin of photocatalytic deactivation of ceria-doped samples prepared by wet impregnation, the as-prepared catalysts were precisely characterized by a variety of complementary methods, providing information about their composition, structure, texture, optical and electronic properties.

To confirm presence of cerium species on the niobia surface, chemical composition of catalysts was analyzed with the use of ICP-OES. As can be seen from Table 1, for all ceriacontaining catalysts, real loading of Ce was only slightly lower than the assumed values and was found to be of 0.7, 3.7 and 7.9 wt.% of Ce for Ce1/Nb2O5, Ce5/Nb2O5 and Ce10/Nb2O5, respectively. Structure of materials was characterized by powder X-ray diffraction (λ = 1.5406 Å).

As can be seen from Fig. 4, PXRD patterns of all samples exhibited two distinct diffraction peaks at 22.7 and 46.3 ° 2θ, which are similar to the reported PXRD pattern of deformed orthorhombic Nb2O5 phase [START_REF] Murayama | Hydrothermal Synthesis of Octahedra-Based Layered Niobium Oxide and Its Catalytic Activity as a Solid Acid[END_REF] . It should be noted that no crystalline CeO2 or other cerium species was identified for all ceria-doped materials, indicating that ceria species existed in amorphous form or were highly dispersed on niobia surface. our Nb2O5 model against PXRD data from each sample collected with a Si internal standard revealed a slight compression of the c-parameter of the niobia structure with increasing Ce loading (see Table 2). The highest decrease in the c-parameter value was typical of the sample with the highest concentration of ceria dopant, i.e. Ce10/Nb2O5. In view of these observations, we claim that cerium species loaded on Nb2O5 by wet impregnation strongly interacted with the niobia support. and Ce (58), it should be possible to distinguish positions of these two atoms in high resolution HAADF-STEM images. However, no difference in atomic columns contrast in HAADF-STEM images was detected, suggesting very high dispersion of cerium species on the niobia surface. Texture of the catalysts was characterized with the use of low-temperature nitrogen adsorption-desorption measurements. As can be seen from Fig. 7a, all isotherms were of type IV(a) indicating mesoporous structure of the catalysts [START_REF] Thommes | Physisorption of Gases, with Special Reference to the Evaluation of Surface Area and Pore Size Distribution (IUPAC Technical Report)[END_REF] . Textural parameters of materials estimated from nitrogen physisorption are summarized in Table 1. The highest BET surface area of 157 m 2 /g was observed for undoped niobium pentoxide. Deposition of cerium species on niobia by wet impregnation led to decrease in the catalysts surface area, but differences between samples were insufficient to justify drastic difference in catalytic activities. The lowest surface area of 143 m 2 /g was characteristic of the catalyst containing the highest amount of ceria dopant, i.e. Ce10/Nb2O5. Fig. 7b shows that loading of ceria on niobia support also had negligible influence on textural properties of the Nb2O5-based samples. All the catalysts exhibited broad pore size distribution ranging from ca. 2 nm to more than 50 nm. Average pore size estimated for all the catalysts from adsorption branch using Barrett-Joyner-Halenda (BJH) method ranged from 8 to 9 nm (see Table 1). The negligible influence of ceria dopant on BET surface area and pore size distribution estimated for the catalysts is further evidence of the high dispersion of cerium species on niobia surface, which is also coherent with the presence of cerium hydroxyls in the IR spectra reported above. According to literature [START_REF] Liu | Correlation of Structural Characteristics with Catalytic Performance of CuO/CexZr1-xO2 catalysts for NO Reduction by CO[END_REF][START_REF] Reddy | Structural Characterization and Catalytic Activity of Nanosized CexM1-xO2 (M = Zr and Hf) Mixed Oxides[END_REF] , these absorption bands are attributed to O 2-→ Ce 4+ charge transfer transitions and inter-band transitions, respectively. As can be seen from Fig. 8a, deposition of cerium species on niobia increased ability of the composite materials to absorb light in the range of wavelengths typical of O 2-→ Ce 4+ charge transfer transitions. It is worth noting that the increase in light absorption observed for ceria-doped samples was proportional to the amount of cerium. The higher concentration of cerium species in the composite material, the higher the Band gap values estimated for undoped Nb2O5 and commercial CeO2 using Tauc's plot method were of 3.22 and 2.96 eV, respectively, and are in agreement with previous literature data concerning optical properties of Nb2O5 [START_REF] Kulkarni | Nanostructured N-Doped Orthorhombic Nb2O5 as an Efficient Stable Photocatalyst for Hydrogen Generation under Visible Light[END_REF][START_REF] Yan | Nb2O5/TiO2 Heterojunctions: Synthesis Strategy and Photocatalytic Activity[END_REF][START_REF] Zhou | Preparation and Spectroscopic Properties of Nb2O5 Nanorods[END_REF] and CeO2 [START_REF] Channei | Photocatalytic Degradation of Methyl Orange by CeO2 and Fe-doped CeO2 Films under Visible Light Irradiation[END_REF][START_REF] Arul | Fabrication of CeO2/Fe2O3 Composite Nanospindles for Enhanced Visible Light Driven Photocatalysts and Supercapacitor Electrodes[END_REF] . Interestingly, composite material prepared by loading 10 wt.% of Ce on niobia by wet impregnation exhibited significantly lower band gap value than that observed for both pristine metal oxides (see Fig. 8b). Such decrease in band gap value of the composite material may result from formation of large quantity of defect sites in the structure of CeO2 (e.g. Ce 4+ ions with neighboring oxygen defects) which shifted the absorption edge of ceria towards higher wavelengths (i.e. lower energy values) [START_REF] Ansari | Gap Engineering of CeO2 Nanostructure Using an Electrochemically Active Biofilm for Visible Light Applications[END_REF] .

To get a deeper insight into oxidation state of metals in the composite materials, the catalysts were characterized by X-ray photoelectron spectroscopy (Fig. 9). Nb 3d region of unmodified Nb2O5 was characterized by two components, namely Nb 3d5/2 and Nb 3d3/2, with the binding energy of 207.3 eV and 210.0 eV, respectively. According to literature [START_REF] Liu | Hexagonal-like Nb2O5 Nanoplates-Based Photodetectors and Photocatalyst with High Performances[END_REF] , these components are assigned to Nb 5+ species in bulk Nb2O5. In the case of ceria-doped samples

[F(R)*hn) prepared by wet impregnation Nb 3d peaks overlapped with the peak typical of Ce 4p3/2. Precise deconvolution of experimental data led us to distinguish these components (see Fig. 9). The only form of niobium species in all heterostructures was Nb 5+ . Deconvolution of Ce 3d spectra of commercial CeO2 allowed distinguishing ten components, namely v0, v, v', v'', v''', u0, u, u', u'', u''' (see Fig. 9). According to literature [START_REF] Bêche | Ce 3d XPS Investigation of Cerium Oxides and Mixed Cerium Oxide (CexTiyOz)[END_REF][START_REF] Pereira-Hernández | Tuning Pt-CeO2 Interactions by High-Temperature Vapor-Phase Synthesis for Improved Reducibility of Lattice Oxygen[END_REF][START_REF] Lei | Surface-Structure Sensitivity of CeO2 Nanocrystals in Photocatalysis and Enhancing the Reactivity with Nanogold[END_REF] , v, v'', v''' and u, u'', u''' are assigned to Ce 4+ species, while v0, v' and u0 and u' are attributed to Ce 3+ species. Analysis of Ce 3d XP spectra of ceria-doped samples prepared by wet impregnation was more complex due to low intensity of peaks at low cerium loadings. To avoid misinterpretation of experimental data we have omitted deconvolution of Ce 3d spectra collected for Ce1/Nb2O5 and Ce5/Nb2O5.

Nevertheless, it is important to stress that Ce 3d spectra recorded for these two samples had different shape than that observed for commercial CeO2. The most important difference can be considered in terms of a very low relative contribution of components characteristic of Ce 4+ species, in particular u''' which is not overlapped with other peaks (see Fig. 9). More information about oxidation state of cerium species in ceria-doped samples was provided by detailed analysis of Ce 3d spectra of Ce10/Nb2O5, for which the signal was the most intense.

As shown in Fig. 9, relative contribution of XP peaks characteristic of Ce 3+ species was significantly more pronounced for Ce10/Nb2O5 than that observed for commercial CeO2. Since FTIR measurements for both samples did not reveal any noticeable IR band typical of methanol molecules adsorbed on Ce 3+ cations, we claimed that higher relative contribution of XP peaks characteristic of Ce 3+ species established for Ce10/Nb2O5 resulted most probably from higher concentration of defect sites in the structure of this catalyst (i.e. Ce 4+ ions surrounded by oxygen vacancies in which electrons are trapped). As it was documented by Baldim et al. [START_REF] Baldim | The Enzyme-like Catalytic Activity of Cerium Oxide Nanoparticles and Its Dependency on Ce 3+ Surface Area Concentration[END_REF] , concentration of defect sites on the surface of CeO2 nanoparticles often increases with decreasing particle size. Since ceria species in all catalysts prepared by wet impregnation were highly dispersed on niobia surface, we claim that high concentration of the above-mentioned defect sites in the structure of these materials is very likely. It is worth noting that our hypothesis is in agreement with results of UV-vis studies, in which significant shift of the absorption edge of Ce10/Nb2O5 towards lower energy values was observed (see Fig. 8b).

To verify whether the ceria doping has any impact on recombination of charge carriers in the composite materials we have performed photoluminescence measurements. According to literature, the photoluminescence emission is mainly originated from radiative recombination of photo-generated electrons and holes trapped in the band tails of semiconductors [START_REF] Georgiev | Optical Properties of Sol-Gel Nb2O5 Films with Tunable Porosity for Sensing Applications[END_REF] . The higher the emission intensity, the higher the efficiency of charge carriers recombination [START_REF] Khan | Ce 3+ -Ion, Surface Oxygen Vacancy, and Visible Light-Induced Photocatalytic Dye Degradation and Photocapacitive Performance of CeO2-Graphene Nanostructures[END_REF] .

Undoped niobium pentoxide exhibited three broad emission peaks with maximum intensity at ca. 380, 425 and 500 nm (Fig. 10). Fig. 10. Photoluminescence spectra of catalysts.

The emission peaks at ca. 380 and 425 nm exhibit energy close to the optical band gap of Nb2O5

(3.22 eV; see Fig. 8b) and may be attributed to near-band gap emission from Nb2O5

(recombination of photo-excited electrons in the Nb 4d conduction band and holes in the in the O 2p valance band of Nb2O5 46 ), while the green emission at ca. 500 nm may be related to the presence of structure defects, such as distorted NbO6 octahedral groups [START_REF] Zhou | Preparation and Spectroscopic Properties of Nb2O5 Nanorods[END_REF][START_REF] Chen | Nb2O5 Improved Photoluminescence, Magnetic and Faraday Rotation Properties of Magneto-Optical Glasses[END_REF] (charge transfer transitions form Nb 5+ 4d 0 state to O 2p orbital of oxygen ions in distorted NbO6 octahedral [START_REF] Zeng | Three-Photon-Excited Upconversion Luminescence of Niobium Ions Doped Silicate Glass by a Femtosecond Laser Irradiation[END_REF] ).

In the case of commercial CeO2, two main broad emission peaks at similar wavelengths as that observed for Nb2O5 can be identified (the first peak at ca. 425 nm and the second one at ca. 500 nm). The energy of the former emission peak (~2.92 eV) is close to the optical band gap of commercial CeO2 (2.96 eV; see Fig. 8b). Thus, this emission peak can be attributed to the direct band to band recombination of charge carriers in CeO2 (recombination of photo-excited electrons in the Ce 4f conduction band and holes in the O 2p valance band of CeO2). According to literature [START_REF] Kumar | One-Step in Situ Synthesis of CeO2 Nanoparticles Grown on Reduced Graphene Oxide as an Excellent Fluorescent and Photocatalyst Material under Sunlight Irradiation[END_REF][START_REF] Hemalatha | Characterization and Optical Properties of Polyvinyl Alcohol-Cerium Oxide Nanocomposite Films[END_REF] , the latter broad emission peak can be attributed to the transitions from electronic energy levels of defects (mainly oxygen vacancies) localized below the Ce 4f band of the CeO2 nanoparticles to the O 2p valence band of CeO2. In the doped samples, loading of cerium species on niobia led to significant increase in emission intensity of composite materials at ca. 425, 500 and 545 nm (Fig. 10). Increased emission at ca. 425 nm may results both from (2.28 eV) is similar to the optical band gap of Ce10/Nb2O5 (optical band gap resulted from the presence of CeO2 species with high concentration of defect sites; Eg ~ 2.52 eV; Fig. 8b). Thus, the increase in intensity of these emission peaks observed for ceria-doped samples may be attributed to improved charge recombination related to transitions from electronic energy levels of defects (mainly oxygen vacancies) localized below the Ce 4f band of the CeO2 nanoparticles to the O 2p valence band of CeO2.

3.3 Discussion on the role of ceria in deactivation of CeO2/Nb2O5 heterostructures Detailed characterization of as-prepared catalysts led us to observe that ceria species loaded on niobia surface by wet impregnation were not only highly dispersed but also strongly interacted with niobia support. As implied by UV-vis and XPS studies, such highly dispersed ceria species are substantially different from bulk CeO2. The heterostructures prepared by wet impregnation exhibited much higher relative concentration of ceria lattice defects which were responsible for changes in electronic and optical properties of cerium species. As revealed by photoluminescence studies, defects sites in ceria lattice not only modified electronic and optical properties of cerium species but they acted also as recombination centers for photo-excited electrons and holes. To shed more light on recombination of the photo-induced charge carries in CeO2/Nb2O5 heterostructures we have predicted theoretically the conduction (ECB) and valence (EVB) band edges of undoped Nb2O5 and commercial CeO2 using the following empirical equations [START_REF] Yan | Nb2O5/TiO2 Heterojunctions: Synthesis Strategy and Photocatalytic Activity[END_REF] :

ECB = X -E e -0.5*Eg (1) EVB = Eg -ECB (2)
where X is the absolute electronegativity of the semiconductor, obtained from the geometric mean of the electronegativity of its constituent atoms (X values for Nb2O5 and commercial CeO2 are 5.55 eV 20 and 5.57 eV 48 , respectively); Eg is the band gap of the semiconductor (3.22 eV and 2.96 eV for Nb2O5 and commercial CeO2, respectively); E e is the energy of free electrons vs. the hydrogen scale (4.5 eV). The calculated conduction band edge potential of Nb2O5 was found to be of -0.56 eV and is more negative than that of commercial CeO2 (-0.41 eV). Corresponding valence band edge potential estimated for Nb2O5 was of 2.66 eV and more positive than that of commercial CeO2 (2.55 eV). We propose that irradiation of mechanical mixture of the metal oxides with UV light resulted in formation of photo-excited electrons (e -) and positively charged holes (h + ) both in CeO2 and Nb2O5. According to the bands edge positions, the as-formed h + were transferred form valence band of Nb2O5 to valence band of commercial CeO2. At the same time, photo-excited electrons from conduction band of Nb2O5 were transferred to conduction band of CeO2. Thus, the band edge alignments in CeO2/Nb2O5 heterostructures resulted in accumulation of both positively charged holes and photo-excited electrons in ceria species. We hypothesize that such accumulation of the charge carriers in ceria promotes their efficient recombination and diminishes the photocatalytic performance of mechanical mixtures of the metal oxides. More pronounced deactivation of the heterostructures prepared by wet impregnation resulted from two unique features of these materials. Firstly, ceria species in these materials were highly dispersed on niobia surface, providing great interface between the dopant and the support, and improving the photo-excited charge carriers transfer from one semiconductor to another. Secondly, such highly dispersed ceria species exhibited high concentration of defect sites which played the role of recombination centers for photo-generated electrons and holes, promoting their efficient recombination (see Fig. 11).

Conclusions

We demonstrated that addition of ceria to niobium pentoxide led to significant decrease in photocatalytic activity of CeO2/Nb2O5 nanostructures. We have established that at any given concentration of cerium species on niobia surface the photocatalytic activity of both Furthermore, the knowledge about the origin of poisoning effect of Nb2O5 by ceria species is important for developing future heterogeneous ceria-doped photocatalysts too. In case of the Nb2O5, a doping with ceria will require a linker promoting a Z-scheme charge transfer (electron or hole) from niobia to ceria and minimizing the ceria/niobia interfaces.

Fig. 1 .

 1 Fig. 1. (a) activity of catalysts in methanol photooxidation at the steady state for 2 h of reaction;

Fig. 2 .

 2 Fig. 2. FTIR spectra of catalysts surfaces at steady state during methanol adsorption under dark

Fig. 3 (

 3 Fig. 3 (a) FTIR spectra of catalysts surfaces recorded at the beginning of photocatalytic

  of formate IR band, a.u. Nb 2 O 5

Fig. 4 .

 4 Fig. 4. PXRD patterns of catalysts normalized to the intensity of (001) peak.

  structure of Nb2O5 proposed by PXRD, electron diffraction (ED), high-angle annular dark field scanning TEM (HAADF-STEM) imaging and annular bright field STEM (ABF-STEM) analyses were performed. The chemical composition and Ce distribution over the samples was confirmed by STEM-EDX elemental mapping. It was found that irrespectively of Ce amount, ceria-doped samples showed similar features as for undoped Nb2O5 (see Figs. 5 and S4, respectively). All samples consisted of needle-type nanostructures with typical dimensions: length around 20-40 nm and diameter 7-10 nm. They were stuck together in a random array, creating nanopores in the volume of the sample. Corresponding ring ED pattern of ceria-doped niobium pentoxide (Fig. 5d insert) can be fully indexed based on proposed orthorhombic Cmmm structure. No extra rings belonging to Ce or Ce-O structures are present in agreement with PXRD data. EDX elemental mapping in STEM mode evidenced homogeneous distribution of cerium species over Nb2O5 sample (Fig. 5b). STEM-EDX and ED studies support conclusion drawn based on PXRD studies regarding amorphous character or very high dispersion of cerium species on niobia surface.

Fig. 5 (

 5 Fig.5 (a) bright field low magnification TEM image of representative ceria-doped sample

Fig. 6

 6 Fig.6 HAADF -STEM and simultaneously acquired ABF-STEM high resolution images along

Fig. 7 .

 7 Fig. 7. (a) Low-temperature nitrogen adsorption-desorption isotherms of catalysts; (b) pore size

  materials ability to absorb light in the range of wavelengths typical of O 2-→ Ce 4+ charge transfer transitions.

Fig. 8 .

 8 Fig. 8. (a) Diffuse-reflectance UV-vis spectra of catalysts; (b) results of band gap estimation

Fig. 9 .

 9 Fig. 9. Nb 3d + Ce 4p (left) and Ce 3d (right) XP spectra of different catalysts studied in this

  photo-excited electrons in the Nb 4d conduction band and holes in the O 2p valence band of Nb2O5, and/or from promoted recombination of photo-generated charged carries in CeO2. The emission energy of the peaks at ca. 500 nm (2.48 eV) and 545 nm

Fig. 11 .

 11 Fig. 11. Schematic representation of charge transfer process resulting in deactivation of ceria-

  photocatalytic process provided by photoluminescence measurements showed that deactivation

Table 1 .

 1 Characteristics of niobia-based catalysts.

	Catalyst	BET surface area	Average pore size a ,	Ce loading b
		[m 2 /g]	[nm]	[wt.%]
	Nb2O5	157	8.8	-
	Ce1/Nb2O5	153	9.0	0.7
	Ce5/Nb2O5	156	8.3	3.7
	Ce10/Nb2O5 143	8.1	7.9
	CeO2 c	-	-	-

a estimated with the use of BJH method from adsorption branch; b determined with the use of ICP-OES; c commercial CeO2

Table 2 .

 2 Calculated unit cell parameter c obtained from Rietveld refinement of PXRD data with Si internal standard.

	Catalyst	c-parameter,	Rwp,	GoF
		[Å]	[%]
	Nb2O5	3.9147(4)	2.84	1.22
	Ce1/Nb2O5	3.9146(3)	2.88	1.24
	Ce5/Nb2O5	3.9076(3)	3.2	1.39
	Ce10/Nb2O5 3.9009(4)	3.56	1.66
	To confirm the novel orthorhombic Cmmm

Acknowledgments

National Science Centre, Poland (Grant No. 2018/28/C/ST5/00255) is acknowledged for the financial support of this work. PXRD studies performed by C.P.H. and K.K. were supported by National Science Foundation DMR-2003783 grant. Lukasz Wolski wishes to thank prof. Marcin Ziolek and Maria Ziolek (Adam Mickiewicz University, Poznań, Poland) for very helpful discussions and Adrian Walkowiak (Adam Mickiewicz University, Poznań, Poland) for nitrogen physisorption measurements.

Appendix A. Supporting Information

FTIR spectra of catalyst surfaces at the beginning of methanol adsorption under dark conditions (Fig. S1); Crystal structure of the derived Nb2O5 model (Cmmm) (Fig. S2); PXRD patterns for Ce/Nb2O5 samples collected with Si (NIST Si 640d) internal standard (Fig. S3); Bright field and HAADF-STEM low magnification images of Nb2O5 sample, and overview bright field HRTEM image and corresponding ED pattern indexed based on orthorhombic Cmmm structure (Fig. S4).

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Vasily S Stolyarov
email: vasiliy.stoliarov@gmail.com

Stephane Pons

Sergio Vlaic

Sergey V Remizov

Dmitriy Shapiro

Christophe Brun

Sergey I Bozhko

Tristan Cren

Tatiana V Menshchikova

Evgueni Chulkov

Dmitry S Shapiro

#,@ Evgeny V Chulkov

Walter V Pogosov

∇, ¶, † † Yuriy E Lozovik

Dimitri Roditchev

Superconducting Long-Range Proximity Effect through the Atomically Flat Interface of a Bi 2 Te 3 Topological Insulator

lations demonstrate that the Pb-wetting layer leads to significant modifications of both topological and trivial electronic states of Bi 2 Te 3 , which are responsible for the observed longrange proximity effect.

Studies of structural and electronic phenomena occurring at the interfaces of two contacting materials are among the most appealing research fields in physics and nanotechnology. By putting two materials together, one can induce at their interface novel electronic properties absent in one or both materials. Famous examples are the formation of a two-dimensional electron gas at the interface between two semiconductors, [START_REF] Delagebeaudeuf | Metal-(n) AlGaAs-GaAs two-dimensional electron gas FET[END_REF] superconductivity appearing at the interface between two insulators, LaAlO 3 and SrTiO 3 , 2 or angle-tuned electronic properties of bi-layer graphene, [START_REF] Novoselov | Electric Field Effect in Atomically Thin Carbon Films[END_REF] to cite a few. [START_REF] Tresca | Chiral Spin Texture in the Charge-Density-Wave Phase of the Correlated Metallic Pb/Si(111) Monolayer[END_REF][START_REF] Dubost | Resistive Switching at the Nanoscale in the Mott Insulator Compound GaTa 4 Se 8[END_REF][START_REF] Biscaras | Two-dimensional superconductivity at a Mott insulator/band insulator interface LaTiO 3 /SrTiO 3[END_REF][START_REF] Wan | Induced superconductivity in high-mobility two-dimensional electron gas in gallium arsenide heterostructures[END_REF][START_REF] Nadj-Perge | Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor[END_REF][START_REF] Menard | Two-dimensional topological superconductivity in Pb/Co/Si(111)[END_REF][START_REF] Ge | Superconductivity above 100 K in singlelayer FeSe films on doped SrTiO 3[END_REF][START_REF] Brun | Remarkable effects of disorder on superconductivity of single atomic layers of lead on silicon[END_REF] Another possibility is the extension of the desired properties into a given material from a "source" material by proximity. In this way, the superconductivity can be induced in normal metals [START_REF] De Gennes | Boundary Effects in Superconductors[END_REF][START_REF] Clarke | The Proximity Effect Between Superconducting and Normal Thin Films in Zero Field[END_REF][START_REF] Le Sueur | Phase Controlled Superconducting Proximity Effect Probed by Tunneling Spectroscopy[END_REF][START_REF] Karapetrov | Direct Observation of Geometrical Phase Transitions in Mesoscopic Superconductors by Scanning Tunneling Microscopy[END_REF][START_REF] Giazotto | Superconducting quantum interference proximity transistor[END_REF][START_REF] Stolyarov | Ex situ elaborated proximity mesoscopic structures for ultrahigh vacuum scanning tunneling spectroscopy[END_REF][START_REF] Stolyarov | Expansion of a superconducting vortex core into a diffusive metal[END_REF][START_REF] Skryabina | Josephson coupling across a long single-crystalline Cu nanowire[END_REF] or even in semiconductors, [START_REF] Qu | Strong Superconducting Proximity Effect in Pb-Bi 2 Te 3 Hybrid Structures[END_REF][START_REF] Cleuziou | Carbon nanotube superconducting quantum interference device[END_REF][START_REF] Cherkez | Electronic properties of Pb islands on graphene: Consequences of a weak interface coupling from a combined STM and ab initio study[END_REF][START_REF] Stolyarov | Josephson current mediated by ballistic topological states in Bi 2 Te 2.3 Se 0.7 single nanocrystals[END_REF] but also a magnetism [START_REF] Wang | Proximity-Induced Ferromagnetism in Graphene Revealed by the Anomalous Hall Effect[END_REF] or an enhanced spin-orbit coupling. [START_REF] Charpentier | Induced unconventional superconductivity on the surface states of Bi 2 Te 3 topological insulator[END_REF][START_REF] Ren | Spin-orbit coupling effects on the stability of two competing structures in Pb/Si(111) and Pb/Ge(111)[END_REF][START_REF] Brand | Spin-resolved band structure of a densely packed Pb monolayer on Si(111)[END_REF][START_REF] Kou | Two-Dimensional Topological Insulators: Progress and Prospects[END_REF] In this respect, the interface between superconductors (S) and a topological insulator (TI) is expected to induce by proximity peculiar properties such as unconventional superconductivity. [START_REF] Qu | Strong Superconducting Proximity Effect in Pb-Bi 2 Te 3 Hybrid Structures[END_REF][START_REF] Charpentier | Induced unconventional superconductivity on the surface states of Bi 2 Te 3 topological insulator[END_REF] Topologically protected surface states [START_REF] Zhang | Topological insulators in Bi 2 Se 3 , Bi 2 Te 3 and Sb 2 Te 3 with a single Dirac cone on the surface[END_REF][START_REF] Hasan | Colloquium: Topological insulators[END_REF][START_REF] Qi | Topological insulators and superconductors[END_REF][START_REF] Fu | Topological Insulators in Three Dimensions[END_REF][START_REF] Moore | Topological invariants of time-reversal-invariant band structures[END_REF][START_REF] Hsieh | A tunable topological insulator in the spin helical Dirac transport regime[END_REF][START_REF] Si | Recent Advances in Tin: From Two-Dimensional Quantum Spin Hall Insulator to Bulk Dirac Semimetal[END_REF][START_REF] Pi | New Class of 3D Topological Insulator in Double Perovskite[END_REF][START_REF] Tian | Spin-Orbit Coupling-Determined Topological Phase: Topological Insulator and Quadratic Dirac Semimetals[END_REF] are not only attractive from the fundamental point of view, such as the realization of Majorana modes, [START_REF] Xu | Experimental Detection of a Majorana Mode in the core of a Magnetic Vortex inside a Topological Insulator-Superconductor Bi 2 Te 3 /NbSe 2 Heterostructure[END_REF][START_REF] Liu | Creating Majorana fermions in topological insulators[END_REF][START_REF] Yano | Magnetic Gap of Fe-Doped BiS-bTe2Se Bulk Single Crystals Detected by Tunneling Spectroscopy and Gate-Controlled Transports[END_REF] but also for spintronics applications, in the view of their robustness and the forbidden backscattering. [START_REF] Beidenkopf | Spatial fluctuations of helical Dirac fermions on the surface of topological insulators[END_REF][START_REF] Sánchez-Barriga | Subpicosecond spin dynamics of excited states in the topological insulator Bi 2 Te 3[END_REF][START_REF] Xue | Temperature Dependence of Spin-Orbit Torques in Nearly Compensated Tb 21 Co 79 Films by a Topological Insulator Sb 2 Te 3[END_REF] The couple Pb/Bi 2 Te 3 is a good candidate for such a study. Bi 2 Te 3 is a three-dimensional (3D) TI showing high electron mobility of topological (surface) states and a relatively low contribution of trivial (bulk) electronic states to the total electron transport . [START_REF] Kou | Two-Dimensional Topological Insulators: Progress and Prospects[END_REF] Single crystals of Bi 2 Te 3 are available, and the atomically clean surface of the material can be prepared in a vacuum by mechanical cleavage. On the other side, Pb is a good candidate to complete the interface since it is a well-known conventional s-wave superconductor with accessible critical temperature T bulk C =7.2 K. Pb remains superconducting in very thin films down to a few atomic layers, [START_REF] Brun | Reduction of the Superconducting Gap of Ultrathin Pb Islands Grown on Si(111)[END_REF][START_REF] Cherkez | Proximity Effect between Two Superconductors Spatially Resolved by Scanning Tunneling Spectroscopy[END_REF][START_REF] Serrier-Garcia | Scanning Tunneling Spectroscopy Study of the Proximity Effect in a Disordered Two-Dimensional Metal[END_REF] and in the form of ultra-small 3D nanostructures, reaching the Anderson limit. [START_REF] Vlaic | Superconducting parity effect across the Anderson limit[END_REF] Transport measurements of Pb/Bi 2 Te 3 hybrid structures revealed the existence of a strong superconducting proximity effect in both c-and a, b-crystallographic directions of Bi 2 Te 3 . [START_REF] Qu | Strong Superconducting Proximity Effect in Pb-Bi 2 Te 3 Hybrid Structures[END_REF] Recent sensitive experiments showed that the superconductivity induced in TI surface layer can be ballistic [START_REF] Stolyarov | Josephson current mediated by ballistic topological states in Bi 2 Te 2.3 Se 0.7 single nanocrystals[END_REF] or even unconventional [START_REF] Charpentier | Induced unconventional superconductivity on the surface states of Bi 2 Te 3 topological insulator[END_REF] and consistent with the order parameter having p x +ip y component.

In this work, we report on local properties of Pb/Bi 2 Te 3 hybrids composed of fewnanometer thick superconducting nano-islands of Pb dispersed on the atomically clean surface of Bi 2 Te 3 ; the latter is wet by an atomically thin amorphous layer of Pb (WL). The local insight is brought by Scanning Tunneling Microscopy and Spectroscopy (STM/STS), providing precious information about local superconducting properties and their spatial evolution, as compared to previously reported global transport properties. [START_REF] Qu | Strong Superconducting Proximity Effect in Pb-Bi 2 Te 3 Hybrid Structures[END_REF][START_REF] Charpentier | Induced unconventional superconductivity on the surface states of Bi 2 Te 3 topological insulator[END_REF] We found that expectedly, the superconducting gap of Pb-nano-islands depends on their thickness. [START_REF] Brun | Reduction of the Superconducting Gap of Ultrathin Pb Islands Grown on Si(111)[END_REF] In contrast, the proximity induced gap in the amorphous-Pbwetting layer on top of Bi 2 Te 3 is robust and almost independent of the distance to the islands. This is not typical for the diffusive proximity regime; it is also at variance with most of previous reports on Pb-coupled systems such as Pb/HOPG, [START_REF] Hwang | Limit to two-dimensional mobility in modulationdoped GaAs quantum structures: How to achieve a mobility of 100 million[END_REF] Pb/InAs, [START_REF] Magnus | Interface properties of PbInAs planar structures for Andreev spectroscopy[END_REF] Pb/amorphous-Pb [START_REF] Serrier-Garcia | Scanning Tunneling Spectroscopy Study of the Proximity Effect in a Disordered Two-Dimensional Metal[END_REF] Pb/Sb(111) [START_REF] Vincent | Strong coupling and periodic potential at the Pb/Sb(111) interface[END_REF] and Pb/graphene 22 in which a rapid decay of superconducting correlations inside the proximity regions was observed. Moreover, in our case, the characteristic energy scale of the proximity induced gap, ∆ amorph W L ∼ 0.55 meV≈ 0.5∆ P b (∆ bulk P b (3K)=1.23 meV, (T bulk c =6.2 K)), [START_REF] Brun | Reduction of the Superconducting Gap of Ultrathin Pb Islands Grown on Si(111)[END_REF] witnesses a powerful proximity effect between the superconducting islands, well consistent with the results of macroscopic measurements [START_REF] Qu | Strong Superconducting Proximity Effect in Pb-Bi 2 Te 3 Hybrid Structures[END_REF] and does not correspond to the previously presented results in Ref. [START_REF] Cherkez | Proximity Effect between Two Superconductors Spatially Resolved by Scanning Tunneling Spectroscopy[END_REF] where native superconducting gap ∆ cryst W L =0.23 meV (crystalline WL T c =1.8 K) was observed.

By considering the numerically simulated detailed electronic structure of the studied system, we point out that the precise mechanism of superconducting proximity is much more subtle than a direct "spreading" of superconducting correlations to the topologically protected surface state of TI. Even one monolayer of Pb dramatically (ML P b =0.286 nm) modifies the electronic structure of Bi 2 Te 3 , leading to a downward band bending [START_REF] Stolyarov | Double Feimpurity charge state in the topological insulator Bi 2 Se 3[END_REF] and, possibly, forming the 2D accumulation layer of the bulk electrons. The detailed picture depends on the number of atomic layers of Pb present on the surface of Bi 2 Te 3 .

Figure 1 provides a summary of the structural properties of studied samples. The topographic STM image in Fig. 1(a) obtained after in-vacuum Bi 2 Te 3 cleavage reveals the atomically clean surface on which typical structural defects [START_REF] Nikitin | Edge and waveguide terahertz surface plasmon modes in graphene microribbons[END_REF][START_REF] Netsou | Identifying Native Point Defects in the Topological Insulator Bi 2 Te 3[END_REF][START_REF] Stolyarov | Disorder-Promoted Splitting in Quasiparticle Interference at Nesting Vectors[END_REF] are observed. A typical dI(V )/dV spectrum measured at the Bi 2 Te 3 surface in a large energy window around the Fermi level is presented in Fig. 1 Dark areas between the islands are amorphous Pb-wetting regions of Bi 2 Te 3 . We expect that the Pb layer under the Pb island is recrystallized thus forming atomically flat lower interface as it was already shown for Pb/Si(111) where an amorphous wetting layer exits between crystallized islands. [START_REF] Feng | Wetting-layer transformation for Pb nanocrystals grown on Si(111)[END_REF] Fig. 1(e)(top panel, blue line) is the profile taken along the white dashed line presented in Fig. 1(d) and (bottom panel, red line) a cross-section taken somewhere on the surface shown in Fig. 1(c(insert)), which correspond to 2.5 min of Pb deposition when we observe just WL. The coloured background reflects the thickness of the amorphous WL (brawn) and the height of individual single-crystal islands (yellow), where 0 corresponds to the atomically smooth surface of the TI.

Figure 2 deals with the spatial distribution of electronic properties of objects under study. Fig. 2(a) shows zero bias conductivity of different regions, provided Pb islands are already formed on the surface after 15 minutes of deposition (Fig. 1(d)). In this case, a pronounced superconducting gap is open both in the islands (A,C) and in the wetting layer (B). Fig. 2(b) shows experimentally measured spatial evolution of dI/dV spectrum along the normal direction to the edge of the island (A) and wetting layer (B) (Fig. 2(a)). It is seen that the superconducting gap in WL drops on the short length scale of the order of a nanometer and then stays essentially constant through the whole WL area between islands. This behaviour is similar to the one reported in Ref. [START_REF] Cherkez | Proximity Effect between Two Superconductors Spatially Resolved by Scanning Tunneling Spectroscopy[END_REF] for Si substrate, but the length scale for the spatial evolution of the gap in the present case is much shorter. In our system gap drops by the factor close to two, while in Ref. [START_REF] Cherkez | Proximity Effect between Two Superconductors Spatially Resolved by Scanning Tunneling Spectroscopy[END_REF] it drops by the factor of nearly four. Typical spectra on Pb island and WL are shown in Fig. 2(c). It should be noted that a typical gapless spectrum of an amorphous WL of lead far from the island was studied in Ref. [START_REF] Serrier-Garcia | Scanning Tunneling Spectroscopy Study of the Proximity Effect in a Disordered Two-Dimensional Metal[END_REF] The amorphous-WL/Si system has the Coulomb blockade effect, similar to what we observe in our TI based system; it indicates the presence of tunnelling junctions between disordered conductors. [START_REF] Rollbühler | Coulomb Blockade of Tunneling between Disordered Conductors[END_REF] The whole scenario is illustrated by Fig 2(d), which shows schematically two islands A and C separated by WL and typical dI/dV spectra in islands and WL between them. From the comparison of superconducting gaps in amorphous WL in the absence of Pb islands and their presence, it is clear that these islands greatly enhance superconducting correlations in WL due to the proximity effect in a substrate.

Figure 3 shows a dependence of the supercon- ducting gap on Pb island thickness. Fig. 3(a) demonstrates the STM topography map and corresponds to many islands. Fig. 3(b) is the ZBC map of a rectangular area marked by the dashed line in Fig. 3(a). Fig. 3(c) shows spectra for islands of several thicknesses, while the inset demonstrates the decrease of a superconducting gap as island thickness decreases explicitly. The results are in a qualitative agreement with previous works [START_REF] Brun | Reduction of the Superconducting Gap of Ultrathin Pb Islands Grown on Si(111)[END_REF][START_REF] Eom | Persistent Superconductivity in Ultrathin Pb Films: A Scanning Tunneling Spectroscopy Study[END_REF][START_REF] Qin | Superconductivity at the Two-Dimensional Limit[END_REF] Pb islands inducing superconducting correlations in the wetting layer since the wetting layer itself is a normal diffusive metal with a proximity gap fast decaying from the island edge, as it was reported in experiments where insulating Si substrates have been used. [START_REF] Brun | Reduction of the Superconducting Gap of Ultrathin Pb Islands Grown on Si(111)[END_REF][START_REF] Serrier-Garcia | Scanning Tunneling Spectroscopy Study of the Proximity Effect in a Disordered Two-Dimensional Metal[END_REF] In contrast, we observe a non-vanishing proximity gap in the wetting layer and attribute it to the proximity It is known that there are two different conductivity channels associated with the surface of a topological insulator Bi 2 Te 3 (see, e.g., Ref. [START_REF] Suh | Fermi-level stabilization in the topological insulators Bi 2 Se 3 and Bi 2 Te 3 : Origin of the surface electron gas[END_REF] ). The channel of the first type is due to topologically protected gapless Dirac states. In contrast, the second type of channel is due to a more conventional two-dimensional electron gas of accumulation layer. The latter is quite common for Bi 2 Te 3 . [START_REF] Suh | Fermi-level stabilization in the topological insulators Bi 2 Se 3 and Bi 2 Te 3 : Origin of the surface electron gas[END_REF] It can be induced by bulk band bending near the surface or by native defects and dangling bonds present on the surface. [START_REF] Suh | Fermi-level stabilization in the topological insulators Bi 2 Se 3 and Bi 2 Te 3 : Origin of the surface electron gas[END_REF] In practice, it is not easy to distinguish between the two conductivity channels. In our system, the topological insulator is covered by the additional layer of Pb, and these two materials have different work functions, which are nearly 4.1 eV for Pb 60,61 and 5.3 eV for Bi 2 Te 3 . 62 Thus, the work function for Bi 2 Te 3 is larger, and this is expected to result in the downward band bending at the Bi 2 Te 3 surface. This phenomenon is schematically illustrated in Fig. 4. Fermi energy E F is between valence band maximum (VBM) and conduction band minimum (CBM) far from the surface, but both of them are shifted downwards at the surface, so that E F can reside above CBM. The additional downward band bending at the surface thus supports the formation of the electron gas of the accumulation layer. A similar band banding effect was described at [START_REF] Zhang | Quantum confinement effects in Pb nanocrystals grown on InAs[END_REF] where Pb/InAs interface was studied.

These arguments are in full agreement with the results of DFT calculations, which are presented in Fig. 5. As shown in Fig. 5, the Note that these oscillations are typical for freestanding Pb monolayer films. [START_REF] Li | Thickness dependent of phase shift between surface energy and work function in Pb ultrathin films[END_REF] In any case, as expected, the work function of Pb/Bi 2 Te 3 is lower than for pure Bi 2 Te 3 (Fig. 5(a)). The surface electronic structure strongly depends on the number of Pb monolayers. The precise mechanism of the superconducting proximity effect might depend on the fine structure of atoms arrangement at the interface. Moreover, the modification of electronic structure underneath the amorphous wetting layer must also be different from underneath the islands. Thus, we expect that Pb islands placed on topological insulator Bi 2 Te 3 induce supercon-ducting correlations due to the proximity effect. The correlations can be associated with two conductivity channels, either by Dirac electrons or by the electrons of the accumulation layer formed due to the band bending. The two types of electronic surface states have approximately the same Fermi velocities, [START_REF] Chen | Robustness of topological order and formation of quantum well states in topological insulators exposed to ambient environment[END_REF] which for Bi 2 Te 3 are estimated as v F ∼ 5 • 10 5 m/s. [START_REF] Zhang | Topological insulators in Bi 2 Se 3 , Bi 2 Te 3 and Sb 2 Te 3 with a single Dirac cone on the surface[END_REF][START_REF] Beidenkopf | Spatial fluctuations of helical Dirac fermions on the surface of topological insulators[END_REF] The expression, which allows us to estimate superconducting coherence length in both the Dirac and conventional two-dimensional electron gases, is

K Г M 1ML Pb Bi Te 2 3 K Г M 2ML Pb Bi Te 2 3 K Г M 3ML Pb Bi Te
ξ = hv F ∆ T I ,
where ∆ T I ∼ 1 meV is the proximity induced superconducting gap in the topological insulator. We assumed that the contact between Pb and the topological insulator is highly transparent [START_REF] Qu | Strong Superconducting Proximity Effect in Pb-Bi 2 Te 3 Hybrid Structures[END_REF][START_REF] Stanescu | Proximity effect at the superconductor-topological insulator interface[END_REF][START_REF] Zhang | Proximity-effect-induced superconductivity in Bi 2 Te 3 /FeSe 0.5 Te 0.5 thin-film heterostructures with different interface conditions[END_REF] that justifies our estimate for ξ, as follows from the solution of Bogoliubov-de Gennes equations, 69 so that gaps in Pb and at the surface are of the same order. Actually, this is exactly what we see in STM experimentsthe superconducting gap at the wetting layer is approximately twice lower than in Pb islands.

Since superconducting correlations at the wetting layer are induced from the underlying topological insulator surface, we may conclude that the gap under the wetting layer is not smaller. Thus, the coherence length at the topological insulator surface is estimated to be as long as ξ ∼ 1 µm. Moreover, this length due to conductivity within the Dirac channel must be larger than the length due to the two-dimensional electron gas, since v F for Dirac states is of the same order but still larger. Of course, this is an oversimplified picture. At the same time, the actual situation might be more subtle and, in particular, dependent on the details of the arrangement of Pb atoms at the interface. Our simple estimates follow that ξ, within any of the two channels, exceeds by one or two orders in magnitude typical distance between Pb islands. These proximity induced superconducting correlations cover the whole space between islands and, as a result, support the superconductivity in the wetting layer of Pb. The additional evidence of the suggested mechanism comes from the comparison with the results of Refs., [START_REF] Brun | Reduction of the Superconducting Gap of Ultrathin Pb Islands Grown on Si(111)[END_REF][START_REF] Hong | Decay mechanisms of excited electrons in quantum-well states of ultrathin Pb islands grown on Si(111): Scanning tunneling spectroscopy and theory[END_REF][START_REF] Ustavshchikov | Tunneling interferometry and measurement of the thickness of ultrathin metallic Pb(111) films[END_REF][START_REF] Altfeder | Electron Fringes on a Quantum Wedge[END_REF][START_REF] Su | Correlation between Quantized Electronic States and Oscillatory Thickness Relaxations of 2D Pb Islands on Si(111)-( 7 × 7) Surfaces[END_REF] where similar Pb islands grown on Si substrate have been studied by STM. These studies revealed specific features in dI/dV spectra on top of the islands attributed to quantum-well states and the formation of two-dimensional bands. However, such features was not observed in our case, can bee linked to the islands' connection to the conducting substrate.

In summary, we demonstrated a selforganized Pb/Bi 2 Te 3 structure and investigated the local conductance spatial distribution at the interface between superconducting Pb and bulk topological insulator. Pb forms islands grown on atomically clean surfaces of Bi 2 Te 3 as well as an amorphous wetting layer between individual islands. An anomalously strong superconducting proximity effect between Bi 2 Te 3 and wetting layer is revealed, attributed to superconducting correlations induced in topological insulator by Pb islands. We argued that there might be at least two conductivity channels associated with the surface of Bi 2 Te 3 , either due to Dirac electrons or the accumulation layer's normal electrons, formed by the downward band bending at the surface. DFT calculations indeed have shown that the presence of Pb monolayers at the surface of Bi 2 Te 3 leads to the modification of surface electronic structure, which strongly depends on the number of layers. Thus, our results suggest that a detailed arrangement of Pb atoms at the surface of Bi 2 Te 3 must be considered to describe induced superconductivity in this topological insulator adequately.

Methods. The experiments were performed in ultra-high vacuum (UHV, base pressure <2×10 -10 mbar). Five nominal monolayers (ML) of Pb were deposited at room temperature at the deposition rate 1 Å/min onto in vacuum cleaved surface of Bi 2 Te 3 single crystals. STM/STS measurements were performed at 1.3 K in the same UHV environment. Local tunneling conductance dI(V, x, y)/dV spectra were obtained by the numerical derivative of the raw I(V, x, y) data.

Electronic structure calculations were carried out within the density functional theory using the projector augmented-wave method [START_REF] Blöchl | Projector augmented-wave method[END_REF][START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF] as implemented in the VASP. [START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF] To describe the exchange-correlation energy, we used the generalized gradient approximation (GGA) with the PBE functional. [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] In addition, the Hamiltonian contained scalar relativistic corrections, and the spin-orbit coupling was taken into account by the second variation method. [START_REF] Koelling | A technique for relativistic spin-polarised calculations[END_REF] The film calculations presented in this work were performed using symmetric setups, so the upper and lower surfaces are identical. The work function values for the Pb films of 1,2 and 3 ML's on top of Bi 2 Te 3 were calculated as the difference between energies of the vacuum and Fermi levels of the corresponding slabs. In the case of clean Bi 2 Te 3 , the value of the work function was estimated as the difference between energies of the vacuum level and valence band maximum of the slab. [START_REF] He | Work function of (001) and (00-1) surface of α-Fe2O3[END_REF] of Pb thin films and their dependence on quantum well states. Applied Physics Letters 2007, 90, 013109.

Figure 1 :

 1 Figure 1: Structure of studied Pb/Bi 2 Te 3 hybrids. STM data acquired at 1.3 K: (a) -30 × 30nm 2 STM image of UHV cleaved Bi 2 Te 3 surface obtained before Pb islands deposition; (b) -Averaged STS dI/dV(V) spectra of atomically clean Bi 2 Te 3 surface obtained (red dashed line is linear extrapolation for Dirac point (DP) and vertical black lines determine the value of BVB and BCB energies); (c) -300 × 300nm 2 STM image of Pb islands on the surface of Bi 2 Te 3 after 15 minute of Pb deposition. The Insert depict 100 × 100 nm 2 wetting layer (after 2.5 min of lead deposition). (d) -140 × 140nm 2 STM image of Pb islands -zoom from white dashed square (c); (e) -profile along dashed line cross-section depicted on figure (d) (top panel, blue line) and typical wetting layer roughness on the same scale (bottom panel, red line) taken after 2.5 min of lead deposition (c(insert))

  (b); the position of the Dirac point (DP), the top of the valence band (BVB) and the bottom of the conduction band (BCB) are indicated. Fig. 1(c) presents the STM image of the sample 15 minutes after the deposition of Pb. The Pb-islands form a non-connecting network. Fig. 1(d) is a zoom in on the studied area (in Fig. 1(c) it is indicated by a white square). The islands have a flat top and different heights 1-4 nm (3-13 atomic layers of Pb). The typical lateral size of Pb-islands is 30-40 nm.

Figure 2 :

 2 Figure 2: STS data acquired at 1.3 K. (a) -zero bias conductance map of the same areal as Fig.1(d); (b) -dI/dV(V) spectrum spatial evolution between Pb island (A) and Pb-wetting layer (B) deposited on atomically flat surface of Bi 2 Te 3 ; (c) -average spectrum of Pb islands (A, C) and on top of the Pb-wetting layer (B); (d) -3D schematic depiction of the proximity effect distribution at Pb/Bi 2 Te 3 /Pb-wetting layer interface.

Figure 3 :

 3 Figure 3: STM/STS maps acquired at 1.3 K: (a) -800×800 nm 2 STM image of Pb islands on the surface of Bi 2 Te 3 after 15 minute RT deposition of Pb; (b) -zero-bias conductance map of the rectangular area marked by the dashed line on (a); (c) -normalized dI/dV spectrum dependencies as a function of Pb islands thickness (ML), where the black line corresponds to proximised wetting layer. In addition, the insert depicts the behaviour of the Pb superconducting gap (∆) as the inverse thickness of Pb islands varies.

Figure 4 :

 4 Figure 4: Schematic picture of the band bending near the surface of Bi 2 Te 3 .

Figure 5 :

 5 Figure 5: (a,b,c,d) Surface electronic structure of clean Bi 2 Te 3 and with 1, 2 and 3 Pb monolayer films, respectively. Red and blue colours denote the states localized in the Bi 2 Te 3 outer most quintuple layer and the Pb films, respectively. Grey background shows a projection of Bi 2 Te 3 bulk bands onto (0001) surface

( 61 )

 61 Aladyshkin, A. Y. Quantum-well and modified image-potential states in thin Pb(111) films: an estimate for the local work function. Journal of Physics: Condensed Matter 2020, 32, 435001.

Acknowledgement Useful comments by R. S. Akzyanov and A. V. Rozhkov are acknowledged. The STM experiments were carried out with the support of the RSF-ANR (project No. 20-42-09033). T.V.M. acknowledges support from RSF within the research project No. 18-12-00169 [DFT calculations of the Bi 2 Te 3 with Pb MLs]. Yu.E.L. acknowledge Program of Basic Research of HSE.


21

Genome wide association study For each marker: is it associated to trait variation?

0 1 2 M 1 M 1 M 1 M 2 M 2 M 2 Phenotype 0 1 2 M 1 M 1 M 1 M 2 M 2 M

  are scored in case of stress occurrence only • Number of years • Cost • Fixation of positive alleles is slow Horizon 2020 of European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. 10 Marker development EUCLEG: an improved GBS protocol -Choice of restriction enzymes to reduce missing data Horizon 2020 of European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. 11 Marker development Horizon 2020 of European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. 12 Marker development EUCLEG: an improved GBS protocol -Choice of restriction enzymes to reduce missing data -Use of a reference genome sequence: Chen et al. 2020 -Allele frequency of each accession Horizon 2020 of European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. window size) Horizon 2020 of European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. 14 Management of genetic diversity Before EUCLEG: • Overview of world diversity Horizon 2020 of European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. 16 Management of genetic diversity EUCLEG: a revision of diversity overview 400 accessions: landraces and cultivars, dormancy 3 Horizon 2020 of European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. 19 Management of genetic diversity PCA : accessions colored with autumn dormancy score Horizon 2020 of European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. 20 Management of genetic diversity EUCLEG: a revision of diversity overview -Diversity: China < > Europe + America -Diversity: Europe <> America -Structure is not associated to autumn dormancy Horizon 2020 of European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312.

2 Phenotype

 2 Horizon 2020 of European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312.

A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. Horizon 2020 of European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. 8 Genomics assisted breeding -Marker development -Management of genetic diversity -Genome wide association study -Genomic selection Horizon 2020 of European Union: Call 2016, SFS 44 : "A joint plant breeding programme to decrease the EU's and China's dependency on protein imports" | This project has received funding from the European Union's Horizon 2020 Programme for Research & Innovation under grant agreement n°727312. 9 Marker development Before EUCLEG: • Low throughput markers: SSR, AFLP… • 10k SNP array: too expensive • GBS: < 40K markers, risk of missing data

EUCLEG.eu