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Jordan Pack, Yinjie Guo, Ziyu Liu, Bjarke S. Jessen, Luke Holtzman, Song Liu, Matthew Cothrine, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), David G. Mandrus, Katayun Barmak, James Hone, Cory R. Dean

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[Charge-transfer contacts for the measurement of correlated states in high-mobility WSe2](https://mdr.nims.go.jp/datasets/28345929-d126-4ac2-909f-0c495bf53c60)

## Fulltext

Charge-transfer Contact to a High-Mobility Monolayer SemiconductorJ. Pack1, Y. Guo1, Z. Liu1, B.S. Jessen1, L. Holtzman2, S. Liu3, M. Cothrine4, K.Watanabe5, T. Taniguchi6, D.G. Mandrus47, K. Barmak2, J. Hone3, and C.R. Dean1†1Department of Physics, Columbia University, New York, NY 10027, USA2Department of Applied Physics and Applied Mathematics,Columbia University, New York, New York 10027, United States3Department of Mechanical Engineering, Columbia University, New York, NY 10027, USA4Department of Materials Science and Engineering,University of Tennessee, Knoxville, Tennessee 37996, United States5Research Center for Electronic and Optical Materials,National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan6Research Center for Materials Nanoarchitectonics,National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan and7Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States(Dated: October 31, 2023)Two-dimensional (2D) semiconductors, suchas the transition metal dichalcogenides, havedemonstrated tremendous promise for the devel-opment of highly tunable quantum devices. Re-alizing this potential requires low-resistance elec-trical contacts that perform well at low temper-atures and low densities where quantum prop-erties are relevant. Here we present a new de-vice architecture for 2D semiconductors that uti-lizes a charge-transfer layer to achieve large holedoping in the contact region, and implement thistechnique to measure magneto-transport proper-ties of high-purity monolayer WSe2. We mea-sure a record-high hole mobility of 80,000 cm2/Vsand access channel carrier densities as low as1.6× 1011 cm−2, an order of magnitude lowerthan previously achievable. Our ability to real-ize transparent contact to high-mobility devicesat low density enables transport measurement ofcorrelation-driven quantum phases including ob-servation of a low temperature metal-insulatortransition in a density and temperature regimewhere Wigner crystal formation is expected, andobservation of the fractional quantum Hall effectunder large magnetic fields. The charge transfercontact scheme paves the way for discovery andmanipulation of new quantum phenomena in 2Dsemiconductors and their heterostructures.Semiconducting van der Waals materials provide arich and versatile platform to study quantum many-bodyground states. The ability to isolate single monolayerflakes allows direct access to the electron gas, enablingwide-ranging opportunities to both interrogate and ma-nipulate the electronic states[1, 2]. Further opportunitiesfor band engineering arise through spatially periodic elec-trostatic gating, lithographic patterning, and interfac-ing with lattice-mismatched or rotated materials to formhetero- and homobilayers [2, 3]. The transition metaldichalcogendides (TMDs) are the most widely studiedvan der Waals semiconductors due to the material cleanli-ness and unique optoelectronic properties. At low carrierdensities, electron-electron interactions play a dominantrole, since the large effective mass suppresses the kineticenergy relative to the Coulomb energy[4]. A wide rangeof interaction-induced phenomena have been observed inTMDs, including fractional quantum Hall states[5], in-teger and fractional Chern insulators[6–11], and excitoninsulators [12–14]. However, only a small minority ofthese studies have employed electrical transport measure-ments, owing to the difficulty of making Ohmic contactsthat remain transparent at low temperature and at lowcarrier density[15].Making electrical contacts to monolayer TMDs re-quires overcoming the well-known challenges intrinsic tomaking Ohmic contact to any semiconductor, such asSchottky barrier formation and Fermi level pinning[15,16]. Work-function tuned metals can help to reducethe Schottky barrier height, whereas doping the semi-conductor in the contact region can be used to reducethe barrier width. However, techniques typically usedto realize transparent electrical contact to bulk semicon-ductors, such as ion implantation and diffused metal con-tacts, cannot be applied in monolayer TMDs due to theiratomically thin structure[16]. To overcome these limita-tions, contacts made from transferred metals[17–19], vander Waals materials[20], and semimetals[21] have beenapplied to TMDs. Other approaches have used surfacetreatments to fabricate heavily doped contacts[22] or em-ployed selective etches to make edge contacts[23]. Whilethese techniques seek to reduce the effective barrier atthe contacts, no approach has demonstrated high perfor-mance contact to high-mobility monolayer semiconduc-tors at the low temperatures and low densities whereelectron-electron interactions significantly modify elec-tronic properties.Here we demonstrate a novel contact scheme that uti-lizes a van der Waals electron acceptor, α-RuCl3 [24–26],to achieve highly-transparent p-type contact to WSe2.arXiv:2310.19782v1  [cond-mat.mes-hall]  30 Oct 202324 3 2 1VG131211109876VCG0.15 0.10 0.05 0.00VG/d (V/nm)10141013101210111010109108107I (A)VGVCG10 8 6 4 2 0n (1011cm2)0255075100125150175200Rc(k m)104105106R2pt()RuCl3WSe2AuFLGVCGVGcharge transfer channel gateFLGWSe2RuCl3Channel GateSource Draincharge transfer Contact Gatecontact gate contact gateEFp++ p p++p+ p+WSe2FLG RuCl3++- -+FLGWSe2RuCl310 0 10VSD (mV)2500250I (nA)VCG= -13 VVCG= -9 Va b cd e fFIG. 1. Charge-Transfer Contact Architecture. a, Schematic illustration of a WSe2 device integrating charge-transfercontacts. Contact metal is omitted from the diagram to show the WSe2- α-RuCl3 interface. b, Band diagram illustrating theexpected charge redistribution when graphite, WSe2, and α-RuCl3 are brought in contact. The modification of the WSe2 workfunction serves to reduce the Schottky barrier. c, Diagram of a WSe2 device with charge-transfer contacts highlighting thedoping profile and the band alignment between the contacts and channel. Fermi-level pinning is identified at the α-RuCl3 edgewhich limits the contact resistance. d, Two terminal resistance at 1.5 K as a function of VCG and VG. e, Comparison of thedevice response to VG and VCG at 300 mK. Gate voltages are normalized to the corresponding BN thickness d. f, Contactresistance at 300 mK as a function of channel density which remains low over a wide range of density. Shaded region emphasizesdensities below 1.7×1011 cm−2 where the contact resistance exceeds 100 kΩ µm. Inset shows I-V characteristics of the devicevarying the contact gate between -9 V and -13 V in steps of 0.5 V. At the maximum |VCG|, the device shows a linear I-Vresponse.We interface the α-RuCl3 to one side of the WSe2 to in-duce large hole-doping in the contact region, with fewlayer graphite on the opposite side forming a metalliccontact. Introducing both the charge transfer and con-tact layers to the 2D semiconductor by mechanical assem-bly allows us to realize a fully contacted and encapsulated2D semiconductor in an all-van der Waals heterostruc-ture. Charge transfer contact to flux-grown WSe2 [27],allows us to study a higher mobility 2D semiconductorthan all past monolayer and bilayer TMD devices, andwith high performance contacts that persist to an orderof magnitude lower density than those reported in pastgenerations of devices. This allows us to study quantumtransport properties at low carrier densities and under astrong magnetic field where interactions between carriersbecome prominent. We identify a low-density metal-to-insulator transition in a dilute regime where a Wignercrystal is expected to be stabilized. We also report thefirst transport signatures of the fractional quantum Halleffect (FQHE) in monolayer WSe2.Figure 1a shows a cartoon schematic of the charge-transfer contact architecture, in which α-RuCl3 is in-corporated so as to dope only the contact region of ah-BN encapsulated monolayer WSe2 device. As illus-trated in Fig. 1b, the charge-transfer layer modifies theband alignment between the WSe2 and the contact metal(few-layer graphene in this case), reducing the Schottkybarrier[37]. Measurements of separate Hall bar struc-tures in which large area α-RuCl3 uniformly dopes boththe contact and channel regions (see SI) indicate thatcoupling to α-RuCl3 induces a hole density of 3.25×1013cm−2 in the WSe2 layer, with a contact resistance as lowas 1.7 kΩ µm, consistent with this microscopic under-standing.35 4 3 2 1 0n (1011cm2)103104105(cm2/Vs)300 K1.5 K101110121013n (cm2)103104105106(cm2/Vs) This Workml WSe2 2L WSe25L WSe20 5 10 15 20 25rs102104106108(cm2/Vs)n-GaAsp-GaAsAlAs ZnOSi MOSFET100101102Temperature (K)103104105(cm2/Vs)n (1012cm2)-5.66-3.11-1.24-0.73-0.44-0.22100101102t (nm)102104106108(cm2/Vs)n-GaAsp-GaAsAlAsThis Workml grapheneabcdeThis WorkFIG. 2. Transport Properties of Low Density WSe2. a, Hall mobility as a function of density from room temperature to1.5 K. b, Hall mobility from room temperature to 1.5 K at multiple channel densities. c, Comparison of this work with pastmeasurements of low-temperature Hall mobility as a function of carrier density in monolayer and few-layer WSe2 [23, 28–30].Using charge-transfer contacts, higher mobilities are accessible at lower densities. d, Mobility as a function of well thicknessshowing that the mobility realized in monolayer WSe2 exceeds what is possible in traditional quantum wells[31–34] at anequivalent thickness. Dashed line shows the expected t6 scaling of mobility due to interfacial roughness in conventional 2DEGs.The value of mobility shown for graphene is a lower bound. e, Comparison of mobility as a function of rs for this work andother semiconducting 2DEGs[31–33, 35, 36]Figure 1c shows a detailed cross-section diagram of thedevice structure with α-RuCl3 integrated in the contactregion only. The device profile consists of three dopingregions. In the vicinity of the metal contact, α-RuCl3induces high hole doping. In the channel region, the car-rier density is controlled by a channel gate, capable ofvarying the hole density from fully depleted at the bandedge to approximately 5×1012 cm−2. Between these tworegions, a contact gate sets an intermediate hole den-sity, thereby smoothing the transition between the con-tact and channel regions. A detailed description of thefabrication process we use to achieve this structure isgiven in the Methods section.Fig. 1d plots the two-terminal device resistance as afunction of channel gate voltage (VG) and contact gatevoltage (VCG) at 1.5 K. The resistance increases sharplyat the threshold VG where carriers are depleted from thechannel. In contrast, the two terminal resistance changesmuch more slowly with varying VCG. The asymmetry be-tween the sharpness of the change in resistance for thetop gate and contact gate is reflected in the subthresh-old slope, which is 1.2 V/dec for the contact gate com-pared to 7 mV/dec for the channel gate (see SI). Whennormalized by the dielectric thickness (Fig. 1e), the sub-threshold slope of the contact gate still exceeds that ofthe channel gate by nearly a factor of 20. We interpretthe comparatively high subthreshold slope of the contactgate response to be the result of Fermi-level pinning atthe lateral boundary where the α-RuCl3 terminates. Theprimary effect of the gate contact is to mitigate the re-sulting band-bending, illustrated in the schematic in Fig.1c[38, 39].Fig. 1f shows the contact resistance at 300 mK mea-sured by subtracting the bulk resistance contributionfrom the two-terminal resistance, with -13 V applied tothe contact gate. The contact resistance measures ap-proximately 20 kΩ µm at high density and remains nearlyconstant down to 4×1011 cm−2 before sharply increas-4MITWignerDisorder0 2 4 6 8 10 12T (K)102101100xx(h/e2)20253040rs0.0 0.5 1.0 1.5 2.0 2.5 3.0n (1011cm2)0.02.55.07.510.012.515.017.520.0(e2/h)6.5 ×1011cm21.3 ×1011cm21.6abFIG. 3. Low-Density Metal to Insulator Transition. a,Resistivity below 30 K for densities between 1.3×1011 cm−2and 6.5×1011 cm−2 showing a metal to insulator transitionaround 1.6×1011 cm−2. b, Conductivity at 300 mK as a func-tion of channel density. Shaded regions indicate the range ofdensities where a Wigner crystal is expected to be stabilized(blue) and where Anderson localization is expected (green).The critical density for the metal to insulator transition isshown as a dashed line. A dashed line at low density marksthe density of charged defects identified in STM measure-ments of similar crystals [27].ing, rising to approximately 100 kΩ µm at a density of1.7×1011 cm−2. Fig. 1f inset shows two terminal IV re-sponse for varying voltage applied to the contact gate.For large bias we observe linear response, consistent withOhmic contact. We note that the contact resistance islarger than achieved when α-RuCl3 uniformly dopes boththe contact and channel regions. For local contact dop-ing, we believe the resistance is limited by the abilityfor the contact gate to populate carriers at the α-RuCl3boundary. Further improvements in contact resistancecould come from improved gate efficiency or interfacialengineering to soften the doping profile at this junction[40].Figure 2a shows the Hall mobility as a function ofcarrier density from room temperature down to cryo-genic temperatures. At 300 K, the mobility exceeds1000 cm2/V s and remains constant over a wide rangeof density. Below 20 K, the mobility varies non-monotonically with carrier density: it first increaseswith increasing density below 1×1012 cm−2 and then de-creases at higher densities. In high mobility 2DEGs, non-monotonic density dependence has been attributed to thepresence of multiple scattering mechanisms relevant indifferent ranges of density; often, scattering from chargedimpurities is dominant at low densities and other mech-anisms are dominant at high density [41]. Recent trans-port studies of monolayer WSe2 have attributed the de-creasing mobility with increasing density to short-rangescattering from Se vacancies in the WSe2 monolayer[29].Figure 2b shows the temperature dependence of the mo-bility at multiple channel densities. At high tempera-tures, the mobility follows a power law as expected forscattering from optical phonons[18, 42]. The value ofthe exponent varies with density between 0.8-1.6 whichagrees with previous measurements of phonon-limitedmobility in few-layer and monolayer WSe2 [18, 29]. Themobility saturates at low temperatures, likely due to scat-tering from local or remote charged impurities.Figure 2c compares the low-temperature Hall mobilityas a function of carrier density measured in this work withpast measurements of monolayer and few layer WSe2[23, 28–30]. Using monolayers derived from WSe2 crys-tals grown with an optimized flux synthesis method [27]we measure mobilities as high as 80,000 cm2/Vs and amobility edge as low as 1.5×1011 cm−2 at low temper-atures. This is an improvement over past monolayerdevices using different contact schemes and bulk crys-tal qualities which have achieved a maximum mobilityof 25,000 cm2/Vs and reported transport response fordensities above 1.6×1012 cm−2 [29].Fig. 2d shows a comparison plot of mobility vs quan-tum well or layer thickness, t, for a variety of 2DEG sys-tems. In confined quantum wells, the mobility is stronglyaffected by scattering from interfacial roughness, whichcauses mobility to scale as t6[34, 42]. Due to the absenceof interfacial roughness, WSe2 demonstrates a uniquescaling advantage, with the mobility far exceeding thet6 limit for conventional 2DEGs. This suggests that themobility measured in our device is limited by internal orexternal charged impurities and substantial mobility en-hancement in the monolayer limit may still be possible byfurther refinements in WSe2 synthesis or heterostructureassembly[27, 43].The combination of large effective mass, high mobil-ity, extreme confinement and low carrier densities make520 15 10 5 0n (1011cm2)051015202530B (T)2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25510152025Rxx(k)0 10 20 30B (T)1050510(K)100101102 Rxx (k )1 2/3ν=2 6/53/2 3/52/51/3ν1/Rxy(e2/h)-2/3-3/5 -2/5-1/3024681012(K)3.02.52.01.51.00.503/2 4/36/56/5212/33/51/31/32/3 3/53/72/54/32/53/2Rxx/8cbadFIG. 4. Fractional Quantum Hall Effect. a, Rxx as a function of magnetic field and density below 2×1012 cm−2 at 300mK. Data below and above 15 T were measured in different thermal cycles. b, Rxx and 1/Rxy measured at 31.4 T for ν > −2.Rxx is scaled for −1 < ν < 0. Rxx displays minima or zeros at the labelled filling fractions. c, Activation gaps for the observedfractional quantum Hall states in the N=0 level as a function of filling fraction. A linear trend is shown following the expectedscaling of the gap for Laughlin states. d, Magnetic field dependence of the measured activation gap at ν = 2/3. A√B fit isshown as a trend in the data. The intercept at zero magnetic field corresponds to the disorder broadening Γ.monolayer WSe2 a particularly promising platform tohost correlated many body ground states. The expectedinfluence of the Coulomb interaction in determining theelectronic properties of a 2DEG is often characterized bythe parameter rs = m∗/(m0aBκ√πn), where m∗/m0 isthe band mass relative to the bare electron mass, κ is theeffective dielectric constant, and aB is the Bohr radius.Owing to the relatively large band mass (0.45 m0)[44]and low κ (4.5)[4], rs is larger in WSe2 than many other2D semiconductors at the same density. Fig. 2e comparesthe mobility as a function of rs between this work andother well-studied 2D electron systems [31–33, 35, 36].We find that monolayer WSe2 displays high mobility overa large range of rs, similar to AlAs and ZnO devices, andexceeding the range of rs values accessible in Si MOSFETdevices by more than a factor of 2.The low sample disorder together with the ability tomaintain high transparency contact to low electron den-sities allows us to map the low temperature metal toinsulator transition (MIT). Fig. 3a shows the resistiv-ity as a function of temperature at densities between1.3×1011 cm−2 and 6.5×1011 cm−2 where we observe aMIT. The critical density (defined as the density wheredρ/dT changes sign in the low-temperature limit) is ap-proximately 1.6×1011 cm−2 (rs = 26.4).The critical density is near the value of rs where a MIThas been observed in ZnO quantum wells and attributedto the formation of a Wigner crystal[45]. Fig 3b plots theconductivity of the sample at T = 300 mK as a functionof density and highlights the expected mechanisms for in-sulating behavior at these low densities. We estimate therange of density that we might expect disorder-inducedlocalization using the Ioffe-Regel-Mott criterion, Γ = EF[46]. We calculate Γ = 4 K from Shubnikov-de Haas os-cillations (see SI) and find that the density where theIRM criterion is satisfied coincides with the charged im-purity density measured by STM in crystals grown undersimilar conditions (approx. 6×1010 cm−2)[27]. Fig. 3balso identfies the range of densities where a Wigner crys-tal is expected from theoretical estimates (rs > 30)[47].We note that the critical density for the Wigner crystalis higher than the density estimated for the Andersoninsulator, suggesting that formation of a Wigner crystalcould be the origin of the MIT observed in our device.However, DC transport measurements alone cannot un-ambiguously differentiate between a Wigner crystal andlocalization due to disorder. Further studies includingpossibly optical[48] or scanning probe measurements [49]willl be necesssary to resolve the orign of the low densitymobility edge.The robust contact achieved with our charge-transferscheme also allows us to measure the properties of mono-6layer WSe2 under a strong magnetic field where inter-actions are significant due to the suppression of kineticenergy. Figure 4a shows the longitudinal resistance at300 mK as a function of magnetic field and carrier den-sity. We identify the presence of integer quantum Hallfeatures down to ν = 1, and multiple fractional quan-tum Hall features in the N = 0 and N = 1 Landau lev-els (LLs). Integer and fractional quantum Hall statesin monolayer WSe2 were previously identified in bulkcompressibility measurements [5], but their characteristictransport properties were inaccessible due to low perfor-mance contacts at low densities. Fig. 4b shows Rxx and1/Rxy as a function of filling fraction at 31.5 T and 300mK. In the N = 0 level, we observe minima or zerosin the longitudinal resistance at filling fractions ν =2/3,3/5, 1/3, 2/5, and 3/7. Additionally, we see the Hallconductance approaching the quantized values at fillingfractions 2/3, 3/5, and 1/3. To our knowledge, this repre-sents the first transport signature of fully developed FQHstates in any van der Waals material beyond graphene.In the N=1 level, there are resistance minima at fillingfractions ν = 6/5, 4/3, and 3/2 with quantized hall con-ductivity at ν = 6/5.The observed hierarchy of the FQH states in boththe N=0 and N=1 LLs, including the appearance of aneven denominator state in the N=1 level, is in agree-ment with the hierarchy identified in bulk compressibil-ity measurements[5]. In the N=0 LL we can estimate thegaps for the FQH states (Fig 4c,d) from the temperaturedependence of the Rxx minima. The gap magnitude ap-pears to be approximately symmetric around ν = −1/2as expected for Laughlin states. Fitting to the expectedscaling with filling fraction, ∆ = ehmcycB∗ − Γ where Γis the disorder broadening and B∗ = B(1 − 2ν)[50], wefind a disorder broadening of 8 K which is approximatelyconsistent with the value identified from Shubnikov-deHaas oscillations (see SI). Further improvements in de-vice quality will allow for a reduction in the disorderbroadening and enable more thorough characterization ofthe fractional quantum Hall states. At ν = 2/3 the gapmagnitude scales approximately as√B as expected fromthe scaling of the effective composite fermion mass[51].The disorder broadening identified from this fit is ap-proximately 9 K in agreement with the other measuresof Γ.Charge-transfer contacts to monolayer WSe2 have en-abled the characterization of transport properties of amonolayer semiconductor with the highest mobility re-ported to date and access to densities an order of magni-tude lower than previously reported. The improvementin sample and contact quality has revealed a MIT at adensity where a Wigner crystal is expected to form andsignatures of the fractional quantum Hall effect at highmagnetic field. The access to transport properties offractional quantum Hall states – including an even de-nominator state – in a monolayer semiconductor opensthe door to new devices seeking to probe the nature ofexcitations of these correlated ground states. Moreover,the charge-transfer contact architecture presents new op-portunities for engineering the contact interface for fur-ther improvements in contact performance. The abilityto measure the transport properties of highly confined,high mobility carriers opens the door for new quantumdevices where electronic transport can be strongly modi-fied by mismatched material interfaces or artificial devicepatterning.METHODSDevice fabricationBulk WSe2 crystals are grown using a two-step fluxsynthesis in a 1:5 W:Se ratio[27]. The monolayer WSe2,BN dielectrics, and few-layer graphite flakes used to makethe device are mechanically exfoliated from bulk crystalsand identified by optical contrast. Prior to exfoliating α-RuCl3, SiO2 substrates are coated with 1-dodecanol toenable later transfer steps. Silicon chips are placed ontoa hot plate at 160 C and 1-dodecanol is applied to thesurface. After 5 minutes, excess dodecanol is removedand chips are rinsed with isopropyl alcohol before dryingwith N2. Flakes of α-RuCl3 are mechanically exfoliatedonto this substrate and identified with optical contrast.The dual graphite gated monolayer WSe2 heterostruc-tures are assembled from these flakes using the van derWaals dry transfer technique[52] at temperatures rangingfrom 70-180 C using a polycarbonate transfer polymer.After assembly, the heterostructure is released onto a Sil-icon substrate with 285 nm of thermal oxide at 180 C.After stacking, a metal contact gate is deposited ontop of the heterostructure using electron beam lithog-raphy and electron beam evaporation. The metal elec-trodes to contact the gates and graphite contacts are firstetched using a selective reactive ion etch using SF6 andO2 plasmas followed by metal deposition to make elec-trical contact. Finally, the device is etched into a Hallbar geometry using reactive ion etching with SF6 andO2 plasmas. During device fabrication, care is taken toavoid exposing the α-RuCl3 layer to solvents – particu-larly acetone – as this exposure can degrade the surfaceand reduce the magnitude of charge transfer. See sup-plementary material for additional fabrication details anddevice images.MeasurementsTransport measurements were performed in a variabletemperature cryostat with a base temperature of 1.5 Kand in a 3He cryostat with a base temperature of 300 mK.7Four and two terminal resistance measurements were car-ried out using a low-frequency lock-in technique at fre-quencies ranging from 3 Hz-200 Hz. IV characteristicswere measured in DC using a sourcemeter. In all mea-surements, the bottom gate is grounded and the top gateis referred to as VG.ACKNOWLEDGMENTSThis research is primarily supported by US Depart-ment of Energy (DE-SC0016703). Synthesis of WSe2(L.H., S.L., K.B.) was supported by the Columbia Uni-versity Materials Science and Engineering Research Cen-ter (MRSEC), through NSF grants DMR-1420634 andDMR-2011738. A portion of this work was performed atthe National High Magnetic Field Laboratory, which issupported by National Science Foundation CooperativeAgreement No. DMR-2128556 and the State of Florida.D.M. and M.C. acknowledge support from the Gordonand Betty Moore Foundation’s EPiQS Initiative, GrantGBMF9069. K.W. and T.T. acknowledge support fromthe JSPS KAKENHI (Grant Numbers 21H05233 and23H02052) and World Premier International ResearchCenter Initiative (WPI), MEXT, Japan.DATA AVAILABILITYThe data that support the plots within this paper andother findings of this study are available from the corre-sponding author upon reasonable request.COMPETING FINANCIAL INTERESTSThe authors declare no competing financial interests.[1] N. P. Wilson, W. Yao, J. Shan, and X. Xu, Nature 599,383 (2021).[2] K. F. Mak and J. Shan, Nature Nanotechnology , 1(2022).[3] L.-k. Shi, J. Ma, and J. C. W. Song, 2D Materials 7,015028 (2019).[4] S. Larentis, H. C. P. Movva, B. Fallahazad, K. Kim,A. Behroozi, T. Taniguchi, K. Watanabe, S. K. Banerjee,and E. Tutuc, Physical Review B 97, 201407 (2018).[5] Q. Shi, E.-M. Shih, M. V. Gustafsson, D. A. Rhodes,B. Kim, K. Watanabe, T. Taniguchi, Z. Papić, J. Hone,and C. R. Dean, Nature Nanotechnology 15, 569 (2020).[6] T. Li, S. Jiang, B. Shen, Y. Zhang, L. Li, Z. Tao, T. 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