Siwen Zhao

Jinqiang Huang
email: phwang@ust.hk

Valentin Crépel

Xingguang Wu

Tongyao Zhang

Hanwen Wang

Xiangyan Han

Zhengyu Li

Chuanying Xi

Senyang Pan

Zhaosheng Wang

Kenji Watanabe

Takashi Taniguchi

Benjamin Sacépé

Jing Zhang

Ning Wang

Jianming Lu
email: jmlu@pku.edu.cn

Nicolas Regnault
email: nicolas.regnault@phys.ens.fr

Zheng Vitto Han

Probing the fractional quantum Hall phases in valley-layer locked bilayer MoS 2

Semiconducting transition-metal dichalcogenides (TMDs) exhibit high mobility, strong spin-orbit coupling, and large effective masses, which simultaneously leads to a rich wealth of Landau quantizations and inherently strong electronic interactions. However, in spite of their extensively explored Landau levels (LL) structure, probing electron correlations in the fractionally filled LL regime has not been possible due to the difficulty of reaching the quantum limit. Here, we report evidence for fractional quantum Hall (FQH) states at filling fractions 4/5 and 2/5 in the lowest LL of bilayer MoS 2 , manifested in fractionally quantized transverse conductance plateaus accompanied by longitudinal resistance minima. We further show that the observed FQH states sensitively depend on the dielectric and gate screening of the Coulomb interactions. Our findings establish a new FQH experimental platform which are a scarce resource: an intrinsic semiconducting high mobility electron gas, whose electronic interactions in the FQH regime are in principle tunable by Coulomb-screening engineering, and as such, could be the missing link between atomically thin graphene and semiconducting quantum wells.

Introduction

Many-body effects driven by Coulomb interaction can lead to a wealth of incompressible gaps at partial fillings of Landau levels (LL), known as the fractional quantum Hall (FQH) states [START_REF] Laughlin | Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations[END_REF][START_REF] Eisenstein | The fractional quantum Hall effect[END_REF][START_REF] Stormer | The fractional quantum Hall effect[END_REF][START_REF] Feldman | Fractional charge and fractional statistics in the quantum Hall effects[END_REF] . The FQH states are revealed through their edge conduction channels, whose transport exhibits a minimum of longitudinal resistance ρ xx and a transverse conductance σ xy quantized as νe 2 /h, with e and h the elementary charge and the Planck constant, respectively. In the composite fermion theory [START_REF] Jain | Composite-fermion approach for the fractional quantum Hall effect[END_REF][START_REF] Pan | Fractional quantum Hall effect of composite fermions[END_REF][START_REF] Son | The Dirac composite fermion of the fractional quantum Hall effect[END_REF] , the main series of fractions is ν = p/(2kp + 1), with k and p integers, or its particle-hole conjugate partner ν = 1p/(2kp + 1). FQH states are the very first known electronic system that hold promises for topological quantum computations, owing to their non-conventional exchange statistics in the non-Abelian 5/2 states observed in GaAs and ZnO semiconductors [START_REF] Moore | Nonabelions in the fractional quantum Hall effect[END_REF][START_REF] Stern | Anyons and the quantum Hall effect-a pedagogical review[END_REF][START_REF] Lin | Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene[END_REF] . Continuous theoretical efforts have also been devoted to the development of superconducting FQH hybrid systems to engineer parafermions, a generalized version of Majorana fermions, for quantum computing purposes with fractional topological orders [START_REF] Clarke | Exotic non-abelian anyons from conventional fractional quantum Hall states[END_REF][START_REF] Vaezi | Superconducting analogue of the parafermion fractional quantum Hall states[END_REF][START_REF] Alicea | Topological phases with parafermions: Theory and blueprints[END_REF] .

For four decades, researchers have endeavored to search for solid state 2D electron gas (2DEG) systems that exhibit fractionally quantized σ xy plateaus; a handful of them only, such as semiconductor quantum wells [START_REF] Tsui | Twodimensional magnetotransport in the extreme quantum limit[END_REF][START_REF] Tsukazaki | Observation of the fractional quantum Hall effect in an oxide[END_REF][START_REF] Falson | A review of the quantum Hall effects in MgZnO/ZnO heterostructures[END_REF] and graphene [START_REF] Du | Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene[END_REF][START_REF] Dean | Multicomponent fractional quantum Hall effect in graphene[END_REF][START_REF] Feldman | Unconventional sequence of fractional quantum Hall states in suspended graphene[END_REF][START_REF] Maher | Tunable fractional quantum Hall phases in bilayer graphene[END_REF][START_REF] Kou | Electron-hole asymmetric integer and fractional quantum Hall effect in bilayer graphene[END_REF][START_REF] Amet | Composite fermions and broken symmetries in graphene[END_REF] , being reported. The identification of new candidates for FQH remains a fundamental yet challenging pursuit with important consequences. For instance, the SU(4) symmetry breaking of LLs in graphene has lead to unprecedented collective states, including even denominator FQH states in the lowest LL and in higher LLs [START_REF] Li | Even denominator fractional quantum Hall states in bilayer graphene[END_REF][START_REF] Zibrov | Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level[END_REF][START_REF] Kim | Even denominator fractional quantum Hall states in higher landau levels of graphene[END_REF][START_REF] Zibrov | Even-denominator fractional quantum Hall states at an isospin transition in monolayer graphene[END_REF][START_REF] Huang | Valley isospin controlled fractional quantum Hall states in bilayer graphene[END_REF] . Analogously, semiconducting TMDs display a rich variety of interacting phases due to the massive Dirac fermions character of their charge carriers and their strong spin-orbit coupling (SOC) [START_REF] Li | Unconventional quantum Hall effect and tunable spin Hall effect in Dirac materials: Application to an isolated MoS 2 trilayer[END_REF][START_REF] Pisoni | Interactions and magnetotransport through spin-valley coupled landau levels in monolayer MoS 2[END_REF][START_REF] Lin | Determining interaction enhanced valley susceptibility in spin-valley-locked MoS 2[END_REF] .

Recently, Landau levels in mono-or few-layered semiconducting TMDs have been intensively studied experimentally, manifesting giant effective g-factors [START_REF] Lin | Determining interaction enhanced valley susceptibility in spin-valley-locked MoS 2[END_REF][START_REF] Xu | Odd-integer quantum Hall states and giant spin susceptibility in p-type few-layer WSe 2[END_REF][START_REF] Wang | Valley-and spin-polarized landau levels in monolayer WSe 2[END_REF][START_REF] Movva | Density-dependent quantum Hall states and Zeeman splitting in monolayer and bilayer WSe 2[END_REF] , non-conventional sequence of Hall plateaus [START_REF] Wu | Even-odd layer-dependent magnetotransport of high-mobility Q-valley electrons in transition metal disulfides[END_REF][START_REF] Gustafsson | Ambipolar landau levels and strong band-selective carrier interactions in monolayer WSe 2[END_REF] , and LL crossings with possible quantum Hall antiferromagnetic phases [START_REF] Masseroni | Electron transport in dual-gated threelayer MoS 2[END_REF] . Yet most of those studies are far above the quantum limit, i.e. performed at filling fractions ν > 1. Capacitance probes on high-quality monolayer WSe 2 has revealed a series of FQH gaps in the lowest and first excited LLs [START_REF] Shi | Odd-and even-denominator fractional quantum Hall states in monolayer WSe 2[END_REF] , suggesting that fractional quantizations are in principle available in TMDs for transport measurements, which is crucial for the future construction of quantum devices based on the FQH states. Still, fractional quantum Hall plateaus in TMDs, especially in the lowest LLs where electron interactions are the most pronounced, remains elusive. The major challenge lies in the concomitant lack of access to low carrier density close to the band edge, an Ohmic contact to the semiconducting channel at very low temperature, and an appropriate dielectric environment that favours the Coulomb interaction.

In this work, we report evidence for FQH at filling fraction 4/5 and 2/5 in bilayer MoS 2 via transport measurements under high magnetic fields up to 34 T and a base temperature of 300 mK. The technological key that enabled us to measure the FQH effect is new 2D-widowed bismuth contacts that provide Ohmic contacts to ntype MoSe 2 layers, down to the very low carrier density required to reach the quantum limit. Our calculations and measurements consistently suggest that, when subjected to a finite vertical electric field E z , the system behaves very much like a mono-layer MoS 2 whose first four (lowest and first excited) LLs in the conduction band are layer-valley locked, and the spin-degeneracy is fully lifted by the Zeeman energy. The specific LLs spectra of the MoS 2 bilayer, together with the asymmetric Ohmic contact to the high mobility bilayer semiconducting channel, thus provide a unique model to investigate the e-e interactions in the FQH regime.

Results

Windowed Ohmic contact to n-type MoS 2 in the very-low carrier density limit. Although various methods, such as phase-engineered edge contact and the use of Pt or Au bottom electrodes [START_REF] Pisoni | Interactions and magnetotransport through spin-valley coupled landau levels in monolayer MoS 2[END_REF][START_REF] Kappera | Phase-engineered low-resistance contacts for ultrathin MoS 2 transistors[END_REF][START_REF] Cai | Bridging the gap between atomically thin semiconductors and metal leads[END_REF][START_REF] Yuan Liu | Approaching the Schottky-Mott limit in van der Waals metal-semiconductor junctions[END_REF] , have been attempted to establish electrical contact with semiconducting MoS 2 for quantum transport studies, the lowest LL approaching the quantum limit has not yet been possible through transport measurements. Recently, low-melting point metals like Bi and (01 12)-faceted Sb have emerged as potential candidates for forming Ohmic contact to the MoS 2 channel 41 . However, these studies have been limited to relatively high-temperature regimes (above a few tens of Kelvin) thus far. Here, we adopt the bismuth contact method [START_REF] Shen | Ultralow contact resistance between semimetal and monolayer semiconductors[END_REF] , but modify it into a 2D-windowed convention.

We first pre-pattern etched-through windows (with sizes of ∼ 1 × 1 µm 2 ) in few-layered hexagonal boron nitride (h-BN), which are further used as a top BN for encapsulating mono-or bi-layer MoS 2 . The h-BN/MoS 2 /h-BN sandwiches are fabricated in a N 2filled glove box using the dry-transfer method [START_REF] Wang | One-dimensional electrical contact to a twodimensional material[END_REF] . The work-flow of our sample fabrication process is illustrated in Supplementary Figure 1, with several typical samples shown in Supplementary Figure 2. Figure 1a shows an artistic view of the fabricated device. Thermal evaporation of Bi/Au (25 nm/ 30 nm) are carried out after a lithography that exposes the 2D-window opened in the top h-BN. As shown in the optical image of a typical device in Fig. 1b, the 2Dwindowed contact (dashed box in Fig. 1b) is visible for each electrical leads. The device is equipped with top and bottom gates, and etch-shaped into Hall bars for electrical measurements (more details can be found in Methods).

Figure 1c depicts a schematic of the windowed Bi contact on bilayer MoS 2 , providing a cross-sectional view of the shaded section shown in Figure 1a. Clearly, the top surface of MoS 2 is contacted by Bi/Au in a 2D manner, which enables the formation of Ohmic contact to the conduction electrons in semiconducting MoS 2 down to base temperature of sub 1 K. As discussed in Supplementary Figure 3, by applying the transfer length method (TLM), the contact resis- tivity in our devices is estimated to be 450 Ωµm at T = 1.5 K. In the typical dual gated samples, contact areas are doped by only the bottom gate, as illustrated in Fig. 1a-b and Supplementary Figure 4a. Taking sample-BS1 for example, contact resistance is estimated to be a few hundred Ohms by substracting 4-probe resistance from the 2-probe one at 30 mK, as shown in Supplementary Figure 4b. Such a contact resistance is sufficiently low in order to perform quantum transport measurements in the quantum Hall regime. Field effect curves (longitudinal conductance ρ -1 xx as a function of back gate volt-age V bg ) recorded in a typical device BS-1 at different temperatures from 290 K to 300 mK are shown in Fig. 1d. It is seen that the device exhibits enhanced conductivity as the temperature decreases, and the two-terminal I-V curves remain linear at the base temperature of 300 mK (inset in Fig. 1d), suggesting Ohmic contact to the n-type semiconductor. Figure 1e compares the state-of-the-art mobilities obtained in typical TMDs transistors (n-type for MoS 2 and p-type for WSe 2 , respectively) as a function of temperature using different contact methods [START_REF] Jung | Transferred via contacts as a platform for ideal two-dimensional transistors[END_REF][START_REF] Pisoni | Absence of interlayer tunnel coupling of kvalley electrons in bilayer mos 2[END_REF][START_REF] Xu | Odd-integer quantum hall states and giant spin susceptibility in p-type few-layer wse 2[END_REF][START_REF] Wu | Even-odd layer-dependent magnetotransport of high-mobility q-valley electrons in transition metal disulfides[END_REF][START_REF] Chuang | Low-resistance 2d/2d ohmic contacts: a universal approach to high-performance wse2, mos2, and mose2 transistors[END_REF][START_REF] Movva | High-mobility holes in dual-gated wse2 field-effect transistors[END_REF][START_REF] Chuang | High mobility wse2 p-and n-type fieldeffect transistors contacted by highly doped graphene for lowresistance contacts[END_REF][START_REF] Cui | Low-temperature ohmic contact to monolayer mos2 by van der waals bonded co/h-bn electrodes[END_REF] . The electron mobility is estimated to be 10 4 -10 5 cm 2 V -1 s -1 in the typical MoS 2 devices in our work, benchmarking the best performance down to temperatures of sub 1 K. It is thus worth noting that our contact method may promote future applications of high electron mobiliry transistors (HEMT) devices using MoS 2 as a platform, especially at cryogenic temperatures.

LLs of bilayer MoS 2 .

We now study the dual-gated mapping of the channel resistance of typical MoS 2 devices under finite perpendicular magnetic fields B. As shown in Supplementary Figure 5, the dual gate field-effect color maps at B = 12 T and T = 0.3 K are plotted into the parameter space of n and D, with the total carrier density n = (C tg V tg + C bg V bg )/en 0 , and the applied average electric displacement field D = (C tg V tg -C bg V bg )/2ϵ 0 -D 0 , where C tg and C bg are the top and bottom gate capacitances per area, respectively. V tg and V bg are the top and bottom gate voltages, respectively. n 0 and D 0 are residual doping and residual displacement field, respectively. LLs close to the band edges are well developed for both mono-layer (Supplementary Figure 5a) and bilayer (Supplementary Figure 5b) MoS 2 . Landau fan scanned at a fixed D = -0.4 V/nm for the bilayer sample is given in Supplementary Figure 5c. It is seen that the lowest LL can be observed above ∼ 7 T, with the first 5 LLs indexed by fully degeneracy lifted integers ν from 1 to 5. Landau fan spectra measured in the same device but at a fixed V bg = 4.72 V is shown in Fig. 2a. Similar to that in Supplementary Figure 5c, the first 5 LLs are highlighted with dashed white lines, which extrapolate at n ∼ 0 cm -2 , i.e., the band edge. This extremely low carrier density available in our current system allows us to investigate the electronic states below the quantum limit of ν = 1. A line profile of the longitudinal and transverse conductance (defined as inversion format is used for σ xx for better visibility due to the highly resistive ρ xx -more details can be found in Supplementary Figure 6) are plotted in Fig. 2b, the quantization of Hall plateaus for the first 5 LLs can be seen with conductance minima observed in their corresponding σ xx . Higher filling fractions become smeared out and level crossing seems to take place as can be seen in the doping range of n > 1.5 × 10 12 cm -2 , as indicated by solid black arrows in Fig. 2a. Notice that, the LL-crossing can be complicated in multi-layered MoS 2 , as reported previously [START_REF] Li | Unconventional quantum Hall effect and tunable spin Hall effect in Dirac materials: Application to an isolated MoS 2 trilayer[END_REF][START_REF] Lin | Determining interaction enhanced valley susceptibility in spin-valley-locked MoS 2[END_REF][START_REF] Masseroni | Electron transport in dual-gated threelayer MoS 2[END_REF] , but are nevertheless captured to a large extent by our calculations (Supplementary Figure 7). In addition, Fig. 2a displays another set of LL-like features (on the right side of the green dashed line), which is originated from the asymmetric electrical contact to the bilayer MoS 2 , and will be discussed in the coming sections.

σ xx = ρ xx /(ρ
We now consider the LLs of bilayer MoS 2 devices. Their conduction band minima mainly consist of the d z 2 electronic orbitals from both layers and are located at the K and K ′ corners of the Brillouin zone. At these points, the inter-layer hybridization carries non-zero orbital angular momentum and cannot couple the rotationally invariant orbitals of opposite layers. The layer index can therefore be taken as a good quantum number for electrons in the conduction band. Our calculations (Supplementary Note 1) suggest that, a finite vertical electric field E z can split the layer index in the band structure of LLs, with the first four (lowest and first excited) LLs in the conduction band being layer-valley locked. A calculated band structure of LLs at layer polarization energy of E z = 60 meV is given in Fig. 2c, with more details of calculations displayed in the Suppl. Info. To visualize the calculated results, schematics of the first 9 LLs (calculated for B = 40 T and E z = 60 meV) in K and K ′ valley are illustrated in Fig. 2d, which largely differs from the p-doped scenario observed in monolayer WSe 2 [START_REF] Shi | Odd-and even-denominator fractional quantum Hall states in monolayer WSe 2[END_REF] . One key feature of our study is that the Bi/Au electrodes are Ohmically contacted with only one top surface of the bilayer MoS 2 , leading to an asymmetrically-contacted configuration. Unlike the monolayer case (Supplementary Figure 5a), this provides a specific manner to probe the LLs in each of the TMD layer, and enables the observation of LL crossing as shown in dual-gated scan in Fig. 2e and D-n scan in Supplementary Figure 5b. When E z is biased to be sufficiently negative (for example, D < -0.3 V/nm and n < 5× 10 12 cm -2 ), the system effectively behaves as a mono-layer, with the N = 0 and N = 1 LLs being both in the same K-valley and on the top layer but carrying opposite spin polarization. In contrast, when E z is biased to be less negative or even positive, the lowest LLs generically feature a non-zero amplitude on the bottom layer. Due to the asymmetrically-contacted configuration, our measurements only probe a fraction of the total conductivity, leading to interference patterns that perfectly describe the anti-diagonal striped features (indicated by the white dashed lines in Fig. 2e), as also discussed in more details by comparing experimental and simulated results in Supplementary Figure 8 and Supplementary Figures 91011.

FQH plateaus in high quality semiconducting bilayer MoS 2 .

In the following, by applying vertical magnetic field up to 34 T, at T = 300 mK, we examine the QHE in bilayer MoS 2 down to the quantum limit of ν ≤ 1. Figure 3a We then focus on the lowest LL with the magnetic field scanned from 34 T down to 18 T, as shown in Fig. 3c. Dips of R xx corresponding to fractionally quantized transverse conductance develop above ∼ 22 T at filling fractions 4/5 and 2/5. Raw data of R xx at different temperature, and ρ -1

xy at different magnetic fields, are plotted in Fig. 3d and3e, respectively. As a function of temperature, we observe that the kink of R xx at filling fractions of ν = 2/5 rapidly vanishes near 2 K, and that at ν = 4/5 gradually disappears for T up to 8 K. This means the FQH gaps are in the order of a few K at 34 T for the typical bilayer MoS 2 samples in this work. Meanwhile, the plateaus of ρ -1 xy (Fig. 3e) get smeared out below ∼ 26 T, same as that shown in Fig. 3c. It is worth mentioning that the FQH states with denom- inator 5 were reproduced in another typical bilayer MoS 2 sample (BS-6), as shown in Supplementary Figure 12. We further performed temperature dependence measurements of the quantum oscillations of the LLs (Supplementary Figure 13), and the gaps of the first three LLs in the range of B = 10 to 14 T are extracted, as shown in Fig. 3f. Indeed, the gap size of fractionally-charged quasiparticles are smaller compared to those estimated at 34 T at integer filling (Fig. 3f).

The FQH state at 4/5 in MoS 2 bilayers clearly revealed in our transport measurements falls in the universality class of the particlehole (p-h) conjugate of Laughlin's 1/5 state 1 . This state hosts Abelian fractionally-charged quasiparticles, but differs from the fraction 1/3 usually reported to have the largest gap in Laughlin's hierarchy. Our theoretical calculations show that the N = 0 Landau level in MoS 2 bilayers is spanned by radial wavefunctions identical to those of standard semiconducting 2DEGs, and experiences a similar Zeeman effect. We thus expect similar interacting phases in both systems, including FQH states at 1/3 (or its p-h conjugate 2/3). Deviations from this behavior most likely come from non-universal characteristics of the samples, such as disorder, the effective dielectric environment induced by nearby gates, or the axial profile of the wavefunctions related to the finite sample thickness.

We have theoretically modeled the effects of gates and finite thickness as a screening of the Coulomb potential at long and short distances, respectively (see Methods). In the N = 0 Landau level, this screened Coulomb potential is fully specified by its Haldane pseudopotentials V m [START_REF] Haldane | Fractional quantization of the Hall effect: A hierarchy of incompressible quantum fluid states[END_REF] , describing the highest energy that two particles with relative angular momentum m can have in the lowest Landau level (only odd m have an effect on fermionic states). In Fig. 4a, we plot these pseudopotentials at B = 22 T where the 4/5 fraction appears in Fig. 3c for an infinitely thin 2DEG, a monolayer and a bilayer MoS 2 using a realistic gate distance d = 35 nm. The presence of gates yields an exponential decay of V m at large m, much faster than the standard algebraic decay of the unscreened Coulomb potential. As a results, the few lowest pseudopotentials should already capture the physics of our gate-screened samples, and we restrict our attention to the three first ones V m=1,3,5 from now on.

Fig. 4a also points out that the finite thickness of the sample increases V m>1 compared to V 1 . Due to their exact clustering properties, FQH states are sensitive to such changes in the short-range interaction physics. For instance, the ground state of a FQH system at filling 1/3 has perfect overlap with the Laughlin state when V 1 > 0 and all V m>1 = 0, but this overlap decreases as V 3 and V 5 grow [START_REF] Regnault | Evidence of a fractional quantum Hall nematic phase in a microscopic model[END_REF] , as shown in Fig. 4b where we plot this overlap obtained for a finite torus using exact diagonalization (see Methods). For V 3 ≳ 0.5V 1 , this overlap vanishes, signaling a phase transition and a ground state that no longer belongs to the Laughlin universality class. The increase of V m>1 /V 1 in bilayer MoS 2 , observed in Fig. 4a, drives the system to the edge of the phase that has non-zero overlap with Laughlin's 1/3 state, hinting at a potential absence of FQH state at 2/3 in our experiments. Consistent with our experiments, the same calculation at filling 1/5 in Fig. 4c shows that the stability of fractions 1/5, or its p-h conjugate 4/5, barely changes as we go from an infinitely thin 2DEG to a realistic bilayer MoS 2 . In conclusion, while all microscopic details of our samples are not necessarily captured by our calculations, they identify a clear trend that rationalizes the absence of the 2/3 FQH state due to internal screening of the Coulomb potential. It is noticed that for the typical monolayer MoS 2 devices, Laughlin's 1/3 states are also absent, though the hints of FQH states in monolayer samples are exhibiting less well-defined quantization at filling 1/5 compared to the bilayer ones (see Supplementary Figure 14). The observed sensitivity of FQH states to the dielectric environment imposed by nearby gates and by the vertical profile of the heterostructure may allow to engineer a richer phenomenology of FQH states in TMD based heterostructures [START_REF] Papić | Numerical studies of the fractional quantum Hall effect in systems with tunable interactions[END_REF] .

To conclude, we have achieved Ohmic contact to n-type bilayer MoS 2 with extremely low carrier density, and performed systematic transport studies under high magnetic fields up to 34 T and a base temperature of 300 mK. When subjected to a finite vertical electric field E z , the system behaves as a mono-layer MoS 2 whose first four LLs in the conduction band are layer-valley locked, and the spin-degeneracy is fully lifted by the Zeeman shift. The asymmetric Ohmic contact to the high mobility bilayer semiconducting channel allows us to obtain fractionally quantized Hall plateaus of 2/5 and 4/5 in the lowest LL above 26 T, which exhibit negligible tunability against E z , and are at the energy scale of sub 1 K, in agreement with theoretical predictions. Our observation of FQH plateaus in TMDs establishes, after the famed quantum well and graphene, a new material platform for the FQH states-based topological electronic systems. Our research paves the way for low-density transport experiments on TMDs heterostructures, which are necessary to harness the full potential of topological FQH phases, and the promises of their zero-magnetic field analog, the fractional Chern insulators, recently detected in twisted TMD homobilayers [START_REF] Cai | Signatures of fractional quantum anomalous Hall states in twisted MoTe 2[END_REF][START_REF] Zeng | Thermodynamic evidence of fractional Chern insulator in moiré MoTe 2[END_REF][START_REF] Park | Observation of fractionally quantized anomalous Hall effect[END_REF][START_REF] Xu | Observation of integer and fractional quantum anomalous Hall states in twisted bilayer[END_REF] .

Methods

Sample fabrication. vdW few-layers of the h-BN/MoS 2 /h-BN sandwich were obtained by mechanically exfoliating high quality bulk crystals. The vertical assembly of vdW layered compounds were fabricated using the dry-transfer method in a nitrogen-filled glove box. Hall bars of h-BN/MoS 2 /h-BN devices were achieved by plasma etching. Electron beam lithography was done using a Zeiss Sigma 300 SEM with an Raith Elphy Quantum graphic writer. Top gates as well as contacting electrodes were fabricated with a thermal evaporator, with typical thicknesses of Bi/Au ∼ 25/30 nm.

High magnetic field facilities. A hybrid magnet with maximum of 34 T magnetic field and base temperature of 300 mK was used. The facility was equipped with water cooling system, and are maintained by the Steady High Magnetic Field Facilities, High Magnetic Field Laboratory, Chinese Academy of Science.

Electrical measurements. The high precision of current measurements of the devices were measured using a Cascade M150 probe station at room temperature, with an Angilent B1500A Semiconductor Device Parameter Analyzer. Gate voltages on the as-prepared Hall bars were maintained by a Keithley 2400 source meter. During measurements, the TMD layer was fed with an AC I bias of about 10 nA. Low frequency lock-in four-probe measurements were used throughout the transport measurements under high magnetic field and at low temperatures.

Theoretical modellings. The Landau level diagrams for monolayer and bilayer MoS 2 are obtained by applying minimal coupling on the ⃗ k • ⃗ p Hamiltonian for conduction electrons derived from ab-initio simulations. The calculation follows from the formalism of Ref. [START_REF] Zubair | Quantum magnetotransport in bilayer MoS 2 : Influence of perpendicular electric field[END_REF] , which is reviewed in the Suppl. Info. for completeness. We use values of the gap, effective mass, Ising spin-orbit coupling strength in the conduction and valence band, spin and valley g-factors, and uniform interlayer hybridization provided by the first principles calculations of Refs. [START_REF] Kormányos | Spin-orbit coupling, quantum dots, and qubits in monolayer transition metal dichalcogenides[END_REF][START_REF] Fang | Ab initio tight-binding Hamiltonian for transition metal dichalcogenides[END_REF] and rounded off to the millielectronvolt scale.

To describe the interacting phases of our system, we have used the Coulomb potential V(q) = 2πe 2 tanh(qd)/[ϵq(1 + nαqδ)], which faithfully captures the long-distance (small q) and short-distance (large q) asymptotics respectively imposed by gate screening and the out-of-plane structure of MoS 2 multilayers. More precisely, this Coulomb potential reproduces (i) V(q → 0) = 2πe 2 tanh(qd)/(ϵq) expected in presence of gates symmetrically placed at a distance d around the sample, with ϵ ≃ 5 the relative dielectric constant of the surrounding h-BN; and (ii) a Rytova-Keldysh form V(q → ∞) = 2πe 2 /[ϵq(1 + nαqδ)] known to be relevant for TMDs [START_REF] Meckbach | Influence of the effective layer thickness on the ground-state and excitonic properties of transition-metal dichalcogenide systems[END_REF] , with n the number of layers, δ = 0.65 nm the typical interlayer spacing, and α a material specific constant. Note that n = 0 describes an infinitely thin 2DEG with no short-range screening.

Interactions projected to the N = 0 Landau level are accounted for using Haldane's pseudopotentials [START_REF] Girvin | The quantum hall effect: novel excitations and broken symmetries[END_REF] , defined on the plane as V m = (2πℓ 2 B ) -1 ∞ 0 qd qV( q/ℓ B )L m ( q2 )e -q2 with ℓ B the magnetic length, L m the m-the Laguerre polynomial, and V(q) the Coulomb potential. This should be understood as an angular Fourier transformation of the Coulomb potential after projection to the N = 0 Landau level, such that V m energetically penalizes particles with relative angular momentum m. Note that fermions are only sensitive to the odd m pseudopotentials. The FQH state at fraction 4/5 is observed in the magnetic field range 22 -34 T, for which the magnetic length lies between ℓ B ≃ 4.5 -6 nm. Focusing on B = 22 T as in Fig. 4a, the ∼ 35 nm thick boron-nitride layers between our sample and gates yields d/ℓ B ≃ 6, while the coefficient α = 15/ϵ taken from Ref. [START_REF] Van Tuan | Coulomb interaction in monolayer transition-metal dichalcogenides[END_REF] leads to αδ/ℓ B ≃ 0.4. Both of these estimates have been rounded to their first significant digit to highlight their phenomenological nature.

The phase diagrams in Fig. 4b-c were obtained by numerical exact diagonalization of the interacting problem on the torus with a square aspect ratio including the three first pseudo-potentials relevant for fermions V 1 , V 3 and V 5 . We set V 1 = 1 to fix the energy scale. The Hilbert space dimensions for N = 13 particle at filling 1/3 and N = 10 particles at filling 1/5 are 16 020 564 and 20 544 878, respectively, in the momentum sectors of their ground state.

Fig. 1

 1 Fig. 1 Electrical transport in bilayer MoS 2 in the single-particle regime. (a) Schematic illustration of the fabricated device. (b) Optical image of a typical dual-gated bilayer MoS 2 device. One of the 2D contact windows is highlighted by black dashed lines. Scale is 5 µm. (c) Art view of the cross-section at the contact (indicated by the purple window in (a)) of the device under investigation. Bi 25 nm/Au 30 nm electrodes are deposited through the pre-patterned window in the top h-BN. (d) Field effect curves (longitudinal conductance ρ -1 xx v.s. back gate voltage V bg ) of sample-BS1 measured at different temperatures from 290 K to 300 mK. Inset shows the two-terminal I-V curves obtained at T = 300 mK for a channel length of L = 1 µm for different V bg . (e) Summarization of state-of-the-art charge mobilities obtained in TMDs. Electron mobility in MoS 2 obtained in this work is the highest among TMDs transistors using different contact methods.

Fig. 2

 2 Fig. 2 Electrical transport in bilayer MoS 2 in the single-particle regime. (a) Landau fan of sample-BS1 measured at T = 300 mK and V bg = 4.72 V, in the magnetic field range from 0 to 12 T. White dashed lines are guides to eyes, and their crossing point indicates the band edge. (b) Line profile of σ xx = ρ xx /(ρ 2 xx +ρ 2 xy ) and transversal conductance ρ -1 xy at B = 12 T, extracted from (a). (c) Calculated LLs as a function of energy and magnetic field (see details in Methods). (d) Cartoon illustration of the calculated first several LLs at the K and K' valley at B = 40 T and E z = 60 meV. For simplicity, only part of the Brillouin zone is shown. (e) Channel resistance of an asymmetrically contacted bilayer MoS 2 sample device-BS9 as a function of V bg and V tg . Dashed lines are guides to the eye.

Fig. 3

 3 Fig. 3 FQH states of bilayer MoS 2 in the lowest LL in conduction band. (a) σ xx = ρ xx /(ρ 2 xx +ρ 2 xy ), and ρ -1 xy as a function of V tg . V bg is fixed at 5.16 V. (b) ρ -1 xy as a function of V tg , measured for different V bg . (c) Color map of longitudinal conductance measured in the filling fraction range of 0 to 2, and the magnetic field range of 18 to 34 T, at T = 300 mK. (d) Raw data of R xx measured at different temperature. (e) Raw data of ρ -1 xy measured at different magnetic fields. V bg is fixed at 5.16 V in (d) and (e), and data in (a)-(e) are all obtained in bilayer MoS 2 sample-BS10. (f) Gaps of the first three LLs in the range of B = 10 to 14 T in a typical bilayer MoS 2 device (sample-BS7).

Fig. 4

 4 Fig. 4 Numerical investigation of screening effects. (a) Pseudopotential for a gate-screened Coulomb potential in an infinitely thin 2DEG, a monolayer and a bilayer MoS 2 at B = 22 T and a gate-distance d = 35 nm (see Methods for details). We show the pseudopotentials of an unscreened Coulomb potential for comparison. (b) Square overlap between the exact diagonalization ground state |Ψ GS ⟩ and Laughlin's wavefunction |Ψ 1/3 ⟩ numerically computed on a torus with N = 13 electrons at filling fraction 1/3 using three non-zero pseudopotentials V m=1,3,5 . Colored dots shows the values extracted from (a). (c) Same as (b) at filling fraction 1/5 using N = 10 particles. Cartoons in (b) and (c) illustrates 1/3 and 1/5 Laughlin's phase, respectively, with the black dashed lines highlighting the boundary between a Laughlin-like phase (non-zero overlaps, i.e., blue colored area) and a phase where the Laughlin state is absent (vanishing overlaps, i.e., white colored area).

  displays the σ xx = ρ xx /(ρ 2

	xx +ρ 2 xy ) and
	ρ -1 xy as a function of V tg . Quantized plateaus at fractions of 4/5 and
	2/5 are observed in the lowest LL, with a clear minima associated
	in the longitudinal conductance for the former and an emerging one
	for the latter. This makes semiconducting TMDs another platform
	to investigate, via electrical transport, FQH states after a few known
	2DEG systems of quantum wells and graphene. By varying V tg at
	different values of fixed V bg (i.e., different D), it is noticed that the
	FQH states have little dependence on the displacement field within
	the gate voltage range studied, as shown in Fig. 3b. This hints that,
	in agreement with earlier arguments, the observed FQH states are
	layer-polarized.

Acknowledgement N.R. and V.C. are grateful to Z. Papic for fruitful discussions. This work is supported by the National Key R&D Program of China (No. 2022YFA1203903, 2019YFA0307800, and 2021YFA1400100) and the National Natural Science Foundation of China (NSFC) (Grant Nos. 92265203, 12104462, 11974357, U1932151, 12204287, and 11974027). Z.V.H. acknowledges the support of the Fund for Shanxi "1331 Project" Key Subjects Construction. N.W. thanks the support from the Hong Kong Research Grants Council (Project No. AoE/P-701/20). J.L. thanks the Beijing Natural Science Foundation (Grant No. Z190011). K.W. and T.T. acknowledge support from the JSPS KAKENHI (Grant Numbers 20H00354, 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan. B.S. and N.R. acknowledge support from the Quan-tERA II Programme that has received funding from the European Union's Horizon 2020 research and innovation programme under Grant Agreement No 101017733. N.R. was also supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 101020833). The Flatiron Institute is a division of the Simons Foundation. B.S. was supported by the European Union's Horizon 2020 research and innovation program under the ERC grant SUPER-GRAPH No. 866365.

Data Availability

The data that support the findings of this study are available at Zenodo, https://doi.org/10.5281/zenodo.8079020.

Code Availability

Exact diagonalization results were obtained using the open source and publicly available software DiagHam.

Author Contributions

Z.V.H. and S.Z. conceived the experiment and supervised the overall project. S.Z., J.H., X.W., and X.H. carried out device fabrications; S.Z. and J.H. carried out all the electrical transport measurements; Z.L., C.X., S.P, and Z.W. assisted the measurements at high magnetic fields, with H.W. and T.Z. participated; K.W. and T.T. provided high quality h-BN bulk crystals. Z.V.H., S.Z., J.L., N.W., J.Z., B.S., V.C., and N.R. analysed the experimental data. V.C., and N.R. conducted the theoretical modelings and performed first principles calculations. The manuscript was written by Z.V.H. and V.C. with discussion and inputs from all authors.

Additional Information

Competing interests: The authors declare no competing interests.


C Collado

Hélène Pichot

Caroline Delfosse

E Eschevins

Emmanuel Nicolas

Martine Hennequin

Valérie Collado
email: valerie.collado@udamail.fr

Caroline Eschevins

Impact of early childhood caries and its treatment under general anesthesia on orofacial function and quality of life : A prospective comparative study

Keywords: Early childhood caries, children, orofacial dysfunction, general anesthesia, quality of life, occlusal contacts

Background: Early Childhood Caries (ECC) has become a major public health concern worldwide, mostly affecting children from disadvantaged families in increasingly severe forms. This condition has been frequently reported to alter children's nutrition, growth and general development. It negatively impacts their quality of life, through painful episodes and severe eating difficulties. While this period is crucial for oral praxes development, the impact of dental state on oro-facial functions is poorly documented. This study evaluated the impact of ECC and its treatment under general anesthesia on oro-facial functions and quality of life in pre-school children. Material and Methods: The dysfunction and quality of life scores from 25 children with ECC were evaluated before treatment (T0), one month (T1) and three months after treatment (T2), using the Nordic Orofacial Test-Screening (NOT-S) and the Early Childhood Oral Health Impact Scale (ECOHIS), respectively, in comparison with 16 caries-free children. The number and extent of inter-arch dental contacts were also observed. Results: The pre-operative higher NOT-S score observed in children with ECC decreased to reach the control level at T2. The mastication item was the most affected in the ECC group throughout the study. Their mean ECOHIS score also significantly decreased post-operatively and differences remaining between both groups were no longer clinically relevant. In addition, in children with ECC, values of functional inter-arch surfaces tended to increase over the follow-up period. Conclusions: Oro-facial functions and quality of life, altered by ECC, could be restored through a conservative treatment approach. Relations between dental state, orofacial functions and particularly chewing, and nutrition should be investigated further.

e334

Introduction

Dental caries have been considered as the most common chronic health problem in childhood, and dental care is the most prevalent unmet health need in children [START_REF] Newacheck | The unmet health needs of America's children[END_REF][START_REF] Bissar | Factors contributing to severe early childhood caries in south-west Germany[END_REF]. In particular, Early Childhood Caries (ECC), which mostly affects children from disadvantaged families in increasingly severe forms, has become a major public health concern worldwide [START_REF] Academy | Policy on early childhood caries (ECC): classifications, consequences, and preventive strategies[END_REF][START_REF] Bönecker | Trends in dental caries in 1-to 4-year-old children in a Brazilian city between 1997 and 2008[END_REF]. Early onset of ECC is not easy to identify for parents and primary health care providers [START_REF] Long | Pediatricians' assessments of caries risk and need for a dental evaluation in preschool aged children[END_REF], and children mostly visit a healthcare professional in the case of pain and/or infections when the disease is already well established. Treatment under general anesthesia (GA) is thus often the only viable option to ensure quality dental care in pre-cooperative children [START_REF] Eidelman | A comparison of restorations for children with early childhood caries treated under general anesthesia or conscious sedation[END_REF]. Its positive impact on child health and wellbeing is now recognized [START_REF] Jankauskiene | Oral healthrelated quality of life after dental general anaesthesia treatment among children: a follow-up study[END_REF]. The psychosocial, physical and functional consequences of ECC have often been evoked through acute infectious episodes, sleep loss, irritability due to pain, and also eating difficulty [START_REF] Feitosa | The psychosocial effects of severe caries in 4-year-old children in Recife, Pernambuco, Brazil[END_REF][START_REF] Gomes | Impact of oral health conditions on the quality of life of preschool children and their families: a crosssectional study[END_REF]. In particular, the disease has an impact on children's nutrition, growth and development. Affected children are known to display a higher risk of developing iron deficiency anemia than cariesfree children [START_REF] Schroth | Association between iron status, iron deficiency anaemia, and severe early childhood caries: a case-control study[END_REF]. Body Mass Index (BMI) is also affected, although the population with ECC does not have a specific weight distribution, and the link between ECC and obesity is controversial [START_REF] Vania | Early childhood caries underweight or overweight, that is the question[END_REF]. Paradoxically, to date, the relation between dental state and chewing efficiency and their consequences on nutrition and growth have not been investigated in children. However, even in ancient societies, the role of mastication in nutrition was recognized, and recent studies have indeed implied a scientific link between the oral stage and certain subsequent metabolic mechanisms [START_REF] Ranawana | Postmastication digestion factors influence glycemic variability in humans[END_REF]. In adults and adolescents, interactions between dental status and chewing efficiency were also investigated in different situations and in various groups of patients [START_REF] Mazille | Effect of occlusal appliance wear on chewing in persons with Down syndrome[END_REF][START_REF] Godlewski | Effect of dental status on changes in mastication in patients with obesity following bariatric surgery[END_REF]. In particular, adults with multiple untreated carious lesions experienced chewing deficiency, manifested by a decrease in food comminution related to the number of functional posterior teeth, food selection and functional deteriorations in oral-health related quality of life [START_REF] Decerle | Chewing Deficiencies in Adults with Multiple Untreated Carious Lesions[END_REF]. Other studies have correlated the extent of inter-arch contact areas with masticatory performance [START_REF] English | Does malocclusion affect masticatory performance?[END_REF][START_REF] Woda | Adaptation of healthy mastication to factors pertaining to the individual or to the food[END_REF], suggesting that eating difficulties may not only be due to pain in the presence of carious lesions. However, improving the inter-arch relationship by replacing natural teeth with prosthetic dentures did not fully restore masticatory function [START_REF] Bessadet | Impact of removable partial denture prosthesis on chewing efficiency[END_REF]. Chewing function is regulated by neuromotor control through dental sensory receptors [START_REF] Révérend | Anatomical, functional, physiological and behavioural aspects of the development of mastication in early childhood[END_REF], but it is still unknown whether conservative dental treatment, which would preserve most of this sensory information, could lead to more efficient chewing function. Beyond this question, the real role of teeth on nutrition is of interest.

In children, the role of teeth in orofacial function development and maturation, and especially chewing, has been given very little attention, in particular in the preschool period. However, early childhood is a key period for acquiring praxes involved in all orofacial functions. Young children with extensive caries may therefore constitute good models for studying the role of dental state on the development of orofacial functions. A comprehensive screening instrument, the Nordic Orofacial Test-screening (NOT-S) assessing different domains within the orofacial functions, was developed [START_REF] Bakke | Development and evaluation of a comprehensive screening for orofacial dysfunction[END_REF]. This evaluation tool has been used in several studies among different groups of patients, including very young children [START_REF] Bergendal | Profiles of orofacial dysfunction in different diagnostic groups using the Nordic Orofacial Test (NOT-S) -a review[END_REF]. However, very few included the dental state of their subjects. So far, only one study including children and adults with ectodermal dysplasia has demonstrated a negative impact of oligodontia on orofacial function [START_REF] Bakke | Development and evaluation of a comprehensive screening for orofacial dysfunction[END_REF][START_REF] Bergendal | Orofacial dysfunction in ectodermal dysplasias measured using the Nordic Orofacial Test-Screening protocol[END_REF]. Another study on schoolchildren and adolescents with orthodontic needs indicated that orofacial dysfunctions are related to the deterioration of masticatory performance [START_REF] Marquezin | Assessment of masticatory performance, bite force, orthodontic treatment need and orofacial dysfunction in children and adolescents[END_REF]. Within the same age range, masticatory performance was also positively correlated with dental status and with posterior inter-arch contacts [START_REF] De Morais Tureli | Associations of masticatory performance with body and dental variables in children[END_REF][START_REF] Barbosa T De | The relationship between oral conditions, masticatory performance and oral health-related quality of life in children[END_REF]. On the contrary, data obtained from younger children failed to link masticatory performance to the inter-arch contact area [START_REF] Oueis | Factors affecting masticatory performance of Japanese children[END_REF]. Indeed, factors affecting masticatory performance may differ according to the developmental stage of the individual. In the case of early childhood caries, it is possible that praxes involving tongue and lip muscles, still present in young children, could partially offset the deterioration of their dental state. The long-term effect of such possible compensation on orofacial function maturation has yet to be investigated. This study aimed at evaluating the impact of early childhood caries and its conservative rehabilitation under general anesthesia on the frequency and the nature of orofacial dysfunction using the NOT-S questionnaire, and children's Oral Health-Related Quality of life (OHRQoL). The evolution of inter-arch functional contacts participating in mastication was also observed.

Material and Methods

This observational comparative prospective study, designed in accordance with Good Clinical Practice (International Clinical Harmonisation, 1996), was approved by the local ethical committee (CECIC, IRB Number 5044). Parents, or legal guardians, and children received oral and written information explaining the study design and the possible benefits and constraints related to their participation. ASA2, respectively), in need of dental care under GA due to their young age and the number of procedures needed. Inclusion took place during a pre-operative visit (T0) at the Special Dental Care Unit of the University Hospital of Clermont-Ferrand (France) between September 2009 and July 2011. Children with disability, geographical barriers preventing follow-up visits and/or without social security insurance were excluded. The required sample size was estimated from a preliminary study that measured the NOTS score in an ECC group before and after GA. The mean values of the NOTSscore decreased from 1.5 ± 1.2 (before GA) to 0.25 ± 0.71 (one month after GA). Calculations with the epiR package 0.9-30 were based on a difference of 1.25 and a common standard deviation value of 0.9. It indicated the need for at least 22 participants (α = 5%, β = 10%). The control group consisted of children from 2 to 6 years with healthy teeth, included between September and December 2009. These children were recruited within the research laboratory circle, as it was difficult to include children without caries in the hospital setting. The provenance of participants is not supposed to influ-ence the impact of dental health on oro-facial function and quality of life results. Statistical analyses (student-t test, sample size calculation for unequal sample size design) were performed to calculate the adequate sample size for the control group. Consequently, 16 children were included. Medico-social and oral descriptive data are given in table 1 for both groups of children. Both groups were similar in age (t-test) and gender (Fisher exact test). Five out of the 41 children included were slightly over the age limit (71 months) to meet the ECC definition according to the American Association of Pediatric Dentistry (AAPD) [START_REF] Academy | Policy on early childhood caries (ECC): classifications, consequences, and preventive strategies[END_REF]. Two children belonged to the control group (both were 72 months) and three to the experimental group (72, 74 and 75 months respectively). Since these three children had also multiple carious cavities in deciduous teeth, they were included in the "ECC group" in order to simplify the analysis. Furthermore, one child in the control group and four children with ECC had at least one permanent erupting tooth (first molars or central incisors) at T0, and one of them had two cavities in permanent teeth. To describe the children's dental state, the mean decayed/ missing/filled teeth index (dmft) was calculated for both groups. The overall mean dmft score was 9.72±3.22 (min: 4; max: 16) for children with ECC, which corresponds to severe-ECC according to the AAPD3. In children with ECC, an average of 11.9±3.7 teeth per child were treated and 2.6±2.3 teeth were extracted under GA. Treatment under GA was as conservative as possible, in order to maintain sensory information from teeth. Moreover, a causal relationship has been recognized between dento-maxillary dysmorphology and orofacial dysfunction [START_REF] Saccomanno | Causal relationship between malocclusion and oral muscles dysfunction: a model of approach[END_REF]. Thus, to evaluate the real impact of extractions and conservative treatments provided under GA on orofacial function, the presence or absence of orofacial dysmorphology was checked using a simplified version of the Index of Orthodontic Treatment Need (IOTN). This tool specifically measured sagittal, vertical, and transversal dimension abnormalities, as well as dento-maxillary disharmony and crowding [START_REF] Hennequin | Inequalities in oral health for children with disabilities: a French national survey in special schools[END_REF]. No difference was found between either group of children regarding the presence of dysmorphology (Fisher-exact test).

-Data collection For the control group, data collection was carried out during a single evaluation, as the study criteria were not expected to change significantly over the study period. For the ECC group, three visits included in the regular follow-up agenda were scheduled for each child: T0 (pre-operatively), T1 (one month after GA), and T2 (3 months after GA). Two practitioners of the Special Dental Care Unit carried out the consultations for both groups, each involving a clinical examination and an interview with the child and its parents. The data collected concerned socio-demographic information, the children's general health status, oral health information and the study evaluation criteria described further on. Both investigators met before and frequently during the course of the study to harmonize the recording method. * Evaluation criteria -Orofacial dysfunction score (NOT-S score) The main evaluation criterion was the frequency of orofacial dysfunctions evaluated by the Nordic Orofacial Test-Screening (NOT-S), which consisted of a structured interview and a clinical examination [START_REF] Bakke | Development and evaluation of a comprehensive screening for orofacial dysfunction[END_REF]. The French version of the NOT-S was used in this study (http://mun-h-center.se/en/Mun-H-Center/Mun-H-Center-E/NOT-S/). The interview contains 6 domains: (I) sensory function, (II) breathing, (III) habits, (IV) chewing and swallowing, (V) drooling, and (VI) dryness of the mouth. The clinical examination includes 6 domains: [START_REF] Newacheck | The unmet health needs of America's children[END_REF] the face at rest, [START_REF] Bissar | Factors contributing to severe early childhood caries in south-west Germany[END_REF] nose breathing, [START_REF] Academy | Policy on early childhood caries (ECC): classifications, consequences, and preventive strategies[END_REF] facial expression, [START_REF] Bönecker | Trends in dental caries in 1-to 4-year-old children in a Brazilian city between 1997 and 2008[END_REF] masticatory muscle and jaw, [START_REF] Long | Pediatricians' assessments of caries risk and need for a dental evaluation in preschool aged children[END_REF] oral motor function, and [START_REF] Eidelman | A comparison of restorations for children with early childhood caries treated under general anesthesia or conscious sedation[END_REF] speech. Each domain gives a maximum score of one point, even if several items within the same domain are scored positively. The total NOT-S score may vary from 0 to 12.

-Impact of dental caries on quality of life The impact of ECC on child functioning, well-being and Oral Health-Related Quality of Life (OHRQoL) was investigated using a validated French version of the Early Childhood Oral Health Impact Scale (ECOHIS), especially adapted for preschool children [START_REF] Barbosa T De | The relationship between oral conditions, masticatory performance and oral health-related quality of life in children[END_REF]. ECOHIS relies on parental ratings of 13 items grouped into two main parts: part one is the child impact section and consists of four domains: child symptoms (1 item), child functions (4 items), child psychology (2 items), and child self-image and social interaction (2 items). Part two is the family impact section and consists of two domains: parental distress (2 items) and family function (2 items). The scale is scored using a simple Likert frequency type scale, with responses ranging from "Never" to "Very often" (equivalent to scores of 0 to 4) plus a "Don't know" option (also scored 0). Item scores were simply added to create a total scale score that ranged from 0 to 52, with higher scores indicating greater impacts and/or more problems.

-Inter-arch functional contacts The total number of "Functional Units" (TotFU) was defined as the number of pairs of antagonist teeth with at least one contact area during chewing. The child was asked to chew 2-3 cycles on a 200-μm articulating paper [START_REF] Owens | Masticatory performance and areas of occlusal contact and near contact in subjects with normal occlusion and malocclusion[END_REF]. The number of teeth from the lower arch that made at least one colored mark gave the number of TotFU. It was decided not to record potential new contacts from erupting permanent teeth. The maximum TotFU value recorded in fully dentate caries-free young children without dysmorphology was 20. Functional occlusal Surfaces were also registered to specify the extent of the inter-arch contacts, by scanning an elastomeric impression of the inter-dental space with jaws in maximal intercuspidal occlusion. Placed in sitting position on the dental chair, with their head supported by the headrest, the children were trained to close their teeth in the correct position. The silicone paste was first placed with an impression gun on the mandibular arch and the child was encouraged to bite downwards in order to register dental occlusion. Each impression was prepared for scanning using the Silverfast® image analysis software. The OSC (Occlusal Scanning Control) software was then used to determine the surface area (in mm 2 ) of the Total inter-arch Functional Surface (TotFS) for which the silicon thickness ranged from 0 (perforating surface) to 500 μm (near contact surfaces) [START_REF] Owens | Masticatory performance and areas of occlusal contact and near contact in subjects with normal occlusion and malocclusion[END_REF]. The impression of potential permanent teeth was excluded from the analysis. The number of Functional Units and Functional Surfaces was also analyzed separately for both Anterior (incisors and canines) and Posterior (molars) areas (re-e337 spectively number of Anterior and Posterior Functional Units: AntFU and PostFU; Anterior and Posterior Functional Surfaces: AntFS and PostFS).

-Statistical Analysis Data were collected and analyzed using IBM®SPSS® 19 software. The analysis was performed for the 25 children with ECC, except for the inter-arch functional contact criteria for which only 8 complete datasets were obtained (Table 1). This group of 8 children was called "ECC contact" subgroup and it was checked to ascertain whether it was not different from the whole ECC group regarding age, dmft index scores, ECOHIS and NOT-S scores (Student t-test, NS). For each evaluation criterion, the comparison of average values of NOT-S and ECOHIS scores, the number of Functional Units (TotFU, AntFU and PostFU) and the Functional Surfaces (TotFS, AntFS and PostFS) was made between the ECC group and the control group at each evaluation time using a t-test. A paired t-test was used to compare each evaluation criterion within the same ECC group at the different evaluation times.

Results

-Orofacial dysfunction score (NOT-S) In the control group, no dysfunction was scored during the evaluation. The total mean level of dysfunction was significantly higher in the ECC group than in the control group at T0 (t test, p≤0.001) and at T1 (p≤0.05), but decreased significantly between T0 and T1 (p<0.01) so that no difference was observed any longer between the groups at T2 (Table 2). Throughout the study, 18 children from the ECC group out of the 25 decreased their total NOT-S score, 6 maintained their score and one score was increased. The item-by-item intergroup comparison of NOT-S mean scores is shown in table 2. Item IV (chewing and swallowing) was the most prevalent throughout the study (15/25 children at T0, 5/25 at T1 and 4/25 at T2) (Fig. 1). NOT-S items V (drooling), 1 (face at rest) and -Impact on quality of life (ECOHIS) In the control group, no quality of life item was impaired. At T0, the mean ECOHIS score was significantly higher in the ECC group (11.04±7.67) than in the control group (p<0.001) (Table 3). This score decreased significantly between T0 and T1 in the ECC group (p<0.001). However, the difference between groups remained significant until T2 (p<0.001 at T1 and p<0.01 at T2).

In the ECC group, the score of 23 children out of 25 decreased between T0 and T1. At T1 and T2 respectively 7 and 14 children from the ECC group had an ECOHIS score of 0. The item-by-item comparison is presented in table 3.

The most frequent ECOHIS items cited by parents at T0 were "pain" (reported for 19/25 children), "eating difficulty" (15/25), "parents feeling guilty" (18/25) and "parents being upset" (14/25).

-Inter-arch functional contacts (FU and FS)

The mean number of TotFU was lower in the ECC group than in the control group at each evaluation time (p<0.05 at T0 and T2 and p<0.001 at T1). Post-operatively (T1 and T2), the mean number of AntFU remained significantly lower in the ECC group than in the control group (p<0.01 at T1 and p<0.05 at T2). However, the mean number of PostFU remained similar between groups and over time. At T0, the mean values of inter-arch Functional Surfaces (TotFS, AntFS and PostFS) were not different between groups (Table 4). The mean TotFS value was only significantly lower in the ECC group than that in the control group at T1 (p<0.05). In the ECC group, the mean TotFS, PostFS and AntFS values tended to increase after treatment, but the difference with preoperative values was significant only for the anterior area and only at T2 (p<0.05).

Discussion

This study was the first step in exploring the links between dental condition and orofacial function in young children with extensive carious lesions. This analysis objectively assessed the negative impact of ECC on oral function, in particular on children's ability to chew and swallow. It also confirmed the negative influence of ECC on children's quality of life, consistent with recent literature data [START_REF] Jankauskiene | Oral healthrelated quality of life after dental general anaesthesia treatment among children: a follow-up study[END_REF][START_REF] Gomes | Impact of oral health conditions on the quality of life of preschool children and their families: a crosssectional study[END_REF]. Indeed, in our study, children with ECC experienced significant OHRQoL alterations in the symptomatic, functional and psychological domains and in the parents' distress domain. After rehabilitation, the quality of life of children with ECC improved drastically compared to the preoperative evaluation. Although the differences between the two groups remained statistically significant after three months, they were no longer clinically relevant as children had become pain free and reported no eating difficulties (Table 3). It is noteworthy that the ECOHIS scores remained lower than those obtained by other authors for the same population [START_REF] Jankauskiene | Oral healthrelated quality of life after dental general anaesthesia treatment among children: a follow-up study[END_REF]. The greater improvement of quality of life observed in our study may be due to some extent to the very conservative approach of treatments under general anesthesia, possibly restoring functional occlusal contacts, and thus sensory information from teeth.

In our study however, caution is required when interpreting the results concerning the impact of inter-arch contacts on function. Only a very small sample (n=8) e339 could be analyzed because of the difficulty of obtaining an elastomeric impression in a correct occlusion position from these young children with potentially painful teeth. Nonetheless, children with ECC tended to have fewer pairs of antagonist teeth in contact and smaller contact surfaces before treatment than caries-free children, mainly due to tooth decay. During the few months after rehabilitation, occlusal contact surfaces tended to increase to reach the control group level, whereas less functional units remained due to extractions, particularly in the anterior area. One explanation could be that oral function is improved by the restoration of the anatomical support, in turn leading to progressive natural occlusal equilibration. However, additional proof of the benefits for orofacial function obtained from a more or less conservative therapeutic approach in this population is still needed [START_REF]Policy on early childhood caries (ECC): unique challenges and treatment options[END_REF]. Indeed, our study sample was quite homogeneous regarding the extraction rate, and This study is the first to show that dental rehabilitation successfully restores orofacial function in young children, as early as three months after treatment. This result confirmed the capacity of the NOT-S questionnaire to evaluate the outcomes of oral rehabilitation [START_REF] Bergendal | Profiles of orofacial dysfunction in different diagnostic groups using the Nordic Orofacial Test (NOT-S) -a review[END_REF]. One domain related to "chewing and swallowing" was still highlighted post-operatively in ECC children, although the remaining scores were very low. A longer adaptation period may be necessary to restore or develop efficient masticatory function. Another issue is the intervention of a speech therapist to retrain the function and to assist the parents and children to change their feeding habits. Indeed, oro-facial and chewing development may also be compromised in children with ECC because they are not exposed in the first years of childhood to a sufficiently broad range of food textures [START_REF] Gisel | Effect of food texture on the development of chewing of children between six months and two years of age[END_REF]. When mastication is altered, parents probably adapt food choices to their child's capacity and acceptance during food diversification. It is possible that these acquired feeding habits are not naturally modified after rehabilitation. Individual dietary behavior and habits could therefore be influenced in the long-term by early functional deficiencies. Moreover, in children with oral disease, producing a ready-to-swallow food bolus may be difficult and the state of the bolus when finally swallowed remains unknown. Additional studies are necessary to characterize the food bolus of children during their development, as well as the factors influencing bolus granulometry. The complete nutritional risk assessment of these children has not been documented either. Nevertheless, developing efficient mastication during childhood may lead to nutritional benefits in adulthood, as endocrinal pathways induced by the cephalic phase during mastication regulate satiation and bolus comminution, and lead to efficient nutrient uptake [START_REF] Forde | Oral processing characteristics of solid savoury meal components, and relationship with food composition, sensory attributes and expected satiation[END_REF]. Finally, the links between oral condition, oral function and nutritional state must be investigated further by taking a systematic clinical research approach. Assessment of young children's masticatory efficiency, in relation with their dental state, is currently underway through food bolus particle size analysis. This work is the first study to provide an objective assessment of the effect of early childhood caries on orofacial functions, as well as its negative impact on children's quality of life. It also provides evidence of functional restoration through conservative dental treatment approach. This population could be a good model to study the role of dental state in oral function development in children and underlying nutritional aspects.

Fig. 1 .

 1 Fig. 1. Frequency of dysfunctions for each domain of the Nordic Orofacial Test-Screening throughout the study.

Weight (kg) (mean±SD) 18

	Criteria	Control group (n=16)	ECC group (n=25)	ECC contact subgroup (functional contacts recorded) (n=8)
	Ratio girls/boys	5/11	11/14	4/4
	Parents' occupational status (n)	n=32	n=50	n=16
	Managers	28	0	2
	Employees/workers	0	23	8
	Job seekers	0	10	1
	Without work	0	8	4
	others	4	9	1
	Age (months)	57.9±10.5	57.6±12.9	62.1±8.3
	mean±SD (min-max)	(26-72)	(31-75)	(51-75)
		.69±1.8 (n=16)	17.4±2.7 (n=24)	18.5±1.9 (n=8)
	Associated medical condition (n)	0	1 (heart murmur)	0
	Orofacial dysmorphology (n) Sagittal dimension abnormality Vertical dimension abnormality Transversal dimension abnormal-ity Dento-maxillary dysharmony	6 3 3 0 0	13 6 6 0 1	5 3 2 0 0
	dmft index (n teeth)	0	9.7±3.2	8.0±2.7
	d (decayed)	0	9.5±3.2	7.9±2.7
	m (missing)	0	0.2±0.5	0
	f (filled) Dental Treatment (mean±SD) Restorative Endodontics Crowns Extractions	0 -	0.1±0.3 was obtained. 4.2±2.8 -Participants The study group consisted of preschool children (2-6 0.1±0.4 Their informed consent 3.9±3.3 4.4±2.1 4.0±2.4 3.4±1.8 3.3±1.8 years), healthy or with mild systemic disease (ASA1 or 2.6±2.3 1.3±2.1
		e335

Table 1 .

 1 Medico-social and oral descriptive data for each group of children.

	e336

Table 2 .

 2 Comparison of Nordic Orofacial Test-Screening (NOT-S) mean scores between the control group and the ECC group throughout the study.

In the control group, no dysfunction was scored (NOT-S mean score = 0). Significant difference between ECC and control groups (t-test): * p<0.05, ** p<0.01, *** p<0.001. e338 4 (masticatory muscle and jaw) were never scored as altered domains.

Table 3 .

 3 Comparison of Early Childhood Oral Health Impact Scale (ECOHIS) mean scores between the control group and the ECC group throughout the study.

	Frequency of impaired items are reported for the 25 children with ECC. In the control group, no item was scored as impaired
	(ECOHIS mean score = 0).
	Significant difference between ECC and control groups (t-test): * p<0.05, ** p<0.01 *** p<0.001.

Table 4 .

 4 Comparison of Mean Interarch Functional Surfaces and Number of Functional Units throughout the study for both groups. Significant difference between groups (t-test): * p<0.05, ** p<0.01.

		Control	ECC subgroup	ECC subgroup	ECC subgroup
		group	T0	T1	T2
	Interarch functional contacts (mean±SD)
		mean±SD	mean±SD	mean±SD	mean±SD
		(n=16)	(n=8)	(n=8)	(n=8)
	Total Functional Surfaces (TotFS) (mm 2 )	198.31±62,41	154.96±47,73	147.58±41,14*	239.23±149.30
	Anterior Functional Surfaces (AntFS) (mm 2 )	43.96±22,41	30.03±26,46	29.64±17,96	75.54±65.03
	Posterior Functional Surfaces (PostFS) (mm 2 )	154.38±53,56	124.93±39,89	117.94±39.94	163.69±106.46
	Total Functional Units (TotFU)	6.13±2.0,3	4.06±2.52*	2.73±2.25***	4.46±1.71*
	Anterior Functional Units (AntFU)	2.5±1,90	1.38±1,06	0.88±0.84**	1.25±0.89*
	Posterior Functional Units (PostFU)	3.63±0,72	3.25±0,89	3.25±0.89	3±1.07

Acknowledgments

The authors wish to acknowledge Dr. Caroline Gondlach for her technical assistance during certain of the clinical examinations.

Conflict of Interest

The authors declare no conflict of interest.


est destinée au dépôt

  unité de méthanisation territoriale des Hauts-de-France Cette étude a été menée dans un contexte d'épuisement des ressources fossiles, de besoin de réduire les émissions de GES et de répondre aux besoins alimentaires croissants Motivations des agriculteurs à s'engager dans le projet Le projet RESIAR a pour but d'établir les conditions de mobilisation des agro-ressources à des fins nonalimentaires afin qu'elles soient durables et créatrice de valeur ajoutée pour les territoires. Méthodologie : le porteur de projet et 9 sur 30 des agriculteurs interrogés, entretiens semi-directifs Sous quelles conditions socioune dynamique agricole collective se créer autour des projets de valorisation non-alimentaire de la biomasse et quelles gouvernances en émanent?

Processus de décision et dynamique socio-économique des acteurs agricoles dans une filière de méthanisation : cas de la centrale biométhane en Vermandois (Eppeville). Eline Dubarral, Oumayma Essofi, Miravo Rakotovao, Loïc Sauvée To cite this version: Eline Dubarral, Oumayma Essofi, Miravo Rakotovao, Loïc Sauvée. Processus de décision et dynamique socio-économique des acteurs agricoles dans une filière de méthanisation : cas de la centrale biométhane en Vermandois (Eppeville).. Deuxième journée d'études du réseau MéTSHS : "Méthanisation et Territoires", Nov 2019, Paris, France. hal-04280862