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Qi Jun Zong, Haolin Wang, Qi Zhang, Xinle Cheng, Yangchen He, Qiaoling Xu, Ammon Fischer, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Daniel A. Rhodes, Lede Xian, Dante M. Kennes, Angel Rubio, Geliang Yu, Lei Wang

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[Quantum melting of generalized electron crystal in twisted bilayer MoSe2](https://mdr.nims.go.jp/datasets/2cbcb793-8ebc-4534-b08c-7edcf6117e93)

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Quantum melting of generalized electron crystal in twisted bilayer MoSe2Article https://doi.org/10.1038/s41467-025-59365-2Quantum melting of generalized electroncrystal in twisted bilayer MoSe2Qi Jun Zong1,13, Haolin Wang2,3,13 , Qi Zhang1,13, Xinle Cheng4,13,Yangchen He 5, Qiaoling Xu6,7, Ammon Fischer 4, Kenji Watanabe 8,Takashi Taniguchi 9, Daniel A. Rhodes 5, Lede Xian6, Dante M. Kennes4,10,Angel Rubio 10,11 , Geliang Yu 1,12 & Lei Wang 1,12Electrons can form an ordered solid crystal phase ascribed to the interplaybetween Coulomb repulsion and kinetic energy. Tuning these energy scalescandrive aphase transition fromelectron solid to liquid, i.e.,meltingofWignercrystal. Generalized Wigner crystals (GWCs) pinned to moiré superlatticeshave been reported by optical and scanning-probe-based methods. Usingtransport measurements to investigate GWCs is vital to a complete char-acterization, however, still poses a significant challenge due to difficulties inmaking reliable electrical contacts. Here, we report the electrical transportdetection of GWCs at fractional fillings ν = 2/5, 1/2, 3/5, 2/3, 8/9, 10/9, and 4/3in twisted bilayer MoSe2. We further observe that these GWCs undergocontinuous quantum melting transitions to liquid phases by tuning dopingdensity, magnetic and displacement fields, manifested by quantum criticalscaling behaviors. Our findings establish twisted bilayer MoSe2 as a novelsystem to study strongly correlated states of matter and their quantum phasetransitions.The competition and transition between ordered and disorderedphases are central to condensedmatter physics and beyond. Differentstates of matter are often characterized by the presence or absence oflocalized particles, where in the latter case, a liquid phase typicallycomposed of itinerant particles is found. This characterizationfamously includes metal-insulator transitions (MITs)1 and quantumHall states2.Wigner crystals andMott insulators, respectively driven bylong-range Coulomb interaction3,4 and on-site repulsion5, are twoimportant examples for interaction-induced ordered phases. Inprinciple, when quantum fluctuations are strong enough to delocalizethe confined charges, theWigner crystalwillmelt into ametallic phase,referred to as a quantum melting transition6. Similarly, varying theratio of interaction energy to kinetic energy can drive a Motttransition7. Evidences of Wigner crystals have been seen in two-dimensional electron systems (2DES) at very low charge densities,including liquid helium surfaces8, semiconductor heterostructures9,10and 2D materials11–13. However, the tunability of Wigner crystals andMott transitions in these systems remains limited. This necessitates theReceived: 2 October 2024Accepted: 15 April 2025Check for updates1National Laboratory of Solid-State Microstructures, School of Physics and Collaborative Innovation Center of AdvancedMicrostructures, Nanjing University,Nanjing, China. 2School of Advanced Materials and Nanotechnology, Xidian University, Xi’an, China. 3Guangzhou Institute of Technology, Xidian University,Guangzhou, China. 4Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA-Fundamentals of Future Information Technology,Aachen, Germany. 5Department of Materials Science and Engineering, University of Wisconsin, Madison, USA. 6Songshan Lake Materials Laboratory,Dongguan, China. 7College of Physics and Electronic Engineering, Center for Computational Sciences, Sichuan Normal University, Chengdu, China.8Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan. 9Research Center for Materials Nanoarchi-tectonics, National Institute for Materials Science, Tsukuba, Japan. 10Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-ElectronLaser Science (CFEL), Hamburg, Germany. 11Center for Computational Quantum Physics, Simons Foundation Flatiron Institute, New York, USA. 12JiangsuPhysical Science Research Center, Nanjing, China. 13These authors contributed equally: Qi Jun Zong, Haolin Wang, Qi Zhang, Xinle Cheng.e-mail: hlwang@xidian.edu.cn; angel.rubio@mpsd.mpg.de; yugeliang@nju.edu.cn; leiwang@nju.edu.cnNature Communications |         (2025) 16:4058 11234567890():,;1234567890():,;http://orcid.org/0000-0002-5518-5087http://orcid.org/0000-0002-5518-5087http://orcid.org/0000-0002-5518-5087http://orcid.org/0000-0002-5518-5087http://orcid.org/0000-0002-5518-5087http://orcid.org/0000-0002-8786-1465http://orcid.org/0000-0002-8786-1465http://orcid.org/0000-0002-8786-1465http://orcid.org/0000-0002-8786-1465http://orcid.org/0000-0002-8786-1465http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0002-7651-3211http://orcid.org/0000-0003-2060-3151http://orcid.org/0000-0003-2060-3151http://orcid.org/0000-0003-2060-3151http://orcid.org/0000-0003-2060-3151http://orcid.org/0000-0003-2060-3151http://orcid.org/0000-0002-0169-7781http://orcid.org/0000-0002-0169-7781http://orcid.org/0000-0002-0169-7781http://orcid.org/0000-0002-0169-7781http://orcid.org/0000-0002-0169-7781http://orcid.org/0000-0002-1919-9107http://orcid.org/0000-0002-1919-9107http://orcid.org/0000-0002-1919-9107http://orcid.org/0000-0002-1919-9107http://orcid.org/0000-0002-1919-9107http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-59365-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-59365-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-59365-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-59365-2&domain=pdfmailto:hlwang@xidian.edu.cnmailto:angel.rubio@mpsd.mpg.demailto:yugeliang@nju.edu.cnmailto:leiwang@nju.edu.cnwww.nature.com/naturecommunicationsdevelopment of experimental platforms that allow for systematicexaminations of the phase transitions between these and other exoticstates over a broader range of physical parameters.Sparked by recent advances in graphene moiré systems14, moiréstructures utilizing semiconducting transition-metal dichalcogenides(TMDs) have been established as highly tunable systems15–17 that arecapable of capturing the physics of both Wigner crystals18–25 and Mottinsulators26–28. Themoiré-version of a quantummelting transition fromgeneralized Wigner crystals (GWCs) to liquid phases has been theo-retically predicted when the bandwidth surpasses the Coulombrepulsion29–31. Recently, GWCs have been observed in moiré TMDsusing optical detections18,19,32, capacitance measurements33, orscanning-probe-based approaches21,22. These previous efforts focus onthe rigidly crystalline regime to understand the formation ofGWCs16,34,35, yet their quantum transitions to metallic phases have notbeen fully investigated. For instance, whether the quantummelting ofGWCs is of first order or continuous is still under debate30,31,36. Elec-trical transport measurements can provide important signatures forWigner crystals identified by the nonlinear current-voltagecharacteristics10,37 and furnish us to examine the resistance scalingbehaviors in the phase transition process38. Although transportexperiments have shown continuousMott transitions in twisted p-type2D semiconductor WSe239 and aligned heterobilayer WSe2/MoTe240,the observation and quantum melting of GWCs have not yet beenobserved.In this work, we fabricate AA-stacked twisted bilayer MoSe2(tMoSe2), an n-type TMD which allows us to access the moiré physicson the rarely-studied electron-doped side. While the splitting of theconduction band states due to spin-orbit coupling (SOC) in n-typeTMDs is reduced as compared to the valence band states, the effect ofSOC on the moiré physics is expected to be different41,42. Using trans-port measurements, we observe generalized Wigner crystal states atmultiple fractional electron fillings, together with a magnetic fieldstabilized Mott state at ν = 1. The quantum melting of these GWCsstates can be finely controlled by tuning the electric field, magneticfield, or electron density, whereas the Mott state behaves markedlydifferently when changing these parameters.Results and discussionCorrelated states at integer and fractional fillingsFigure 1a shows our dual-gated device structure. Importantly, bismuthis used as themetallization layer to achieve goodohmic contacts43 (see“Methods”). We use polarization-dependent second-harmonic gen-eration (SHG) to determine a twist angle of 4.1∘ (see Extended DataFig. 1). Accordingly, ns, the electron density of half-band filling, is cal-culated to be ~ 6.0 × 1012 cm−2. The moiré filling factor is defined asν = n/ns, where n represents the gate-induced electron density. Thedual-gate device geometry allows independent control over the dis-placement field, D, and electron density, n, via top and back gate vol-tages (VTG and VBG, respectively). Figure 1b shows the longitudinalresistance Rxx as a function of n at VTG = 65 V and T = 1.5 K, in whichpronounced resistance peaks can be observed at ν = 1, 2/3 and 1/2,corresponding to the commensurate fillings of one electron permoiréunit cell, two electrons per threemoiré cells, and one electron per twomoiré unit cells, respectively (See Extended Data Fig. 2 for similar dataobserved in another device). In addition, relatively weaker resistancepeaks at ν = 2/5 and 3/5 are also found. Fig. 1c shows the color map ofRxx versus VTG and VBG, exhibiting features of high resistance tracesalong constant multiple fractional or integer filling lines. Analogousfractional filling states have not been reported so far in hole-dopedmoiré TMDs using transportmeasurement in spite of the observationsthrough optical sensing technique19 or microwave impedancemicroscopy22.To connect to these experimental findings, we perform densityfunctional theory (DFT) calculations. The electronic band structure inFig. 1d confirms the presence of aminiband on the electron side with abandwidth of ~ 70meV for a twist angle close to the experimental oneunder zero (left panel) and large (right panel) D (see SupplementaryMaterials for details). We find that the lowest-lying conduction bandsare faithfully represented by two localized Wannier orbitals centeredat the Se/Mo (Mo/Se) stacking position of themoiré unit cell, which weuse to address the impact of long-ranged Coulomb interactions on theelectronic ordering tendencies of the system on the Hartree-Fock level(see Supplementary Materials for details). It is found that the longerranged interactions are particularly important at fractional fillings andcan stabilize insulating phases with modulated charge patterns on themoiré honeycomb lattice as proposed in the lower cartoons of Fig. 1c.For ν = 1/2, the electrons form a stripe order, and for ν = 2/3, the elec-trons occupy a honeycomb lattice, while for ν = 3/5, the electronsoccupy an elongated honeycomb lattice. Recently, such correlatedstates occurring at fractional fillings ofmoiré superlattices are referredto as generalized Wigner crystals18,19,21,22.Experimentally, we extract the charge gapsof ν = 3/5 and 1/2 statesfrom thermal activations in Fig. 1e (see Extended Data Fig. 3). In theabsence of magnetic fields, the maximal charge gap reaches values of2.2 K (at D =0.11 V/nm), 4.6 K (at D =0.16 V/nm) and 5.2 K (atD = 0.20V/nm) for ν = 2/3, 3/5 and 1/2 states, respectively. We furtheridentify these fractional filling states as GWCs by measuring the dif-ferential resistance, dV/dI, as a function of the applied DC current, IDC(see Extended Data Fig. 4). The differential resistances display strongnonlinear features with pronounced peaks centered at zero IDC. At alowbias, electrons are localized by themoiré superlattice. A bias abovea sufficiently high threshold can lead to a sharp decrease in differentialresistance, which is often referred to as the depinning37 or onset ofsliding of Wigner crystals44.Magnetic and displacement field effectsNext, we investigate the response of the correlated states under theinfluence of external magnetic and displacement fields. By increasingD, the correlated states at fractional fillings turn metallic as the bandsbecome more dispersive, see Fig. 1d. The inset in Fig. 1e shows arepresentativeD-inducedMIT at ν = 3/5. Similar data for the ν = 2/3 and1/2 states are provided in Extended Data Fig. 3. Next, we map out Rxxversus (ν, T) under a large D (VBG = 80V) as shown in Fig. 1f. Theresistance of all correlated states at fractional and integer fillingsincreases as a function of temperature as explicitly shown for ν = 1, 2/3,and 1/2 in the upper penal of Fig. 1g. However, the insulating behavioris recovered in the presence of a strong magnetic field (B = 14 T) asdemonstrated in the lower panel of Fig. 1g. No response to in-planemagnetic field can be observed due to Ising-type SOC26,40 (see Exten-ded Data Fig. 5).Figure 2a shows a series of color maps of Rxx for different mag-netic fields in dependence of D and ν at T = 1.5 K. Both the fractionalfilling and ν = 1 states become more resistive when increasing B. Thetemperature dependence of Rxx depicted in Fig. 2b for the states atν = 1/2 and2/3 unambiguously shows that the applicationof amagneticfield strengthens the insulating behavior. To quantify this, we extractthe magnetic field-dependent charge gaps in Fig. 2c, from which wecan also extract the effective g-factor of the generalizedWigner crystalstates. Interestingly, the g-factor decreases for increasing displace-ment field (bottom panel inset), taking values of g = 1.6 (0.3) at dis-placement fields of D =0.16 (0.65) V/nm.Multiple possible effects can strengthen the insulating behaviorwith applying amagneticfield45–48. Inour system, thebehavior ofGWCsis qualitatively akin to those of the correlated states with the spin-polarized nature in other moiré materials23,48–50. To explain such aneffect, we consider the effect of Zeeman splitting as illustrated inFig. 2d. Zeeman coupling causes an energetic splitting of the spinspecies by an energy EZ = gμBB. Therefore, the spin-polarized corre-lated insulators will experience an increase of their gap when applyingArticle https://doi.org/10.1038/s41467-025-59365-2Nature Communications |         (2025) 16:4058 2www.nature.com/naturecommunicationsa magnetic field. When decreasing D, correlation effects are strongerdue to the reduced bandwidth, as shown in the DFT calculations(Fig. 1d). Therefore, the fractional filling states have a stronger ten-dency of spontaneous spin-polarization induced by correlations. Fig-ure 2e shows the Landau fan diagram at VBG = 90 V, which reveals atwo-fold degenerated Landau levels stemming from the conductionband minimum at K-point51. We observe that the B-field inducedenhancement is found for all GWCs as well as ν = 1 state, which isunable to be predicted by other enhancement mechanisms45–47.Strikingly, additional correlated states emerge at largermagneticfieldsfor fractional fillings of ν = 4/3, andmore faintly, even 8/9 and 10/9. Tofully confirm the nature of their magnetic orders, other optical tech-niques need to be used and will be reported in our future work.Quantum melting transitionsWe examine the temperature dependence of Rxx to determine themetallic or insulating phases in the B − D space (see Extended DataFigs. 6 and 7). As shown in Fig. 3a, the insulating phase occupies mostFig. 1 | Emergence of correlated states at integer and fractional fillings intMoSe2. a Schematic side view (left) and optical image of the device (lower right,the scale bar is 10μm) and depiction of the twisted bilayer MoSe2 moiré super-lattice (upper right). The sign of the displacement field, D, is defined to be positivewhen the field points from the back gate to the twisted sample. b Longitudinalresistance Rxx plotted against carrier density, n, at VBG = 65 V and T = 1.5 K. Thedashed lines mark the moiré filling factor (ν) of each resistive peak. c Color map ofRxx as a function ofVTG andVBG under zero perpendicularmagneticfield (B =0T) at1.5 K. Proposed chargeorders for ν = 1/2 (left), 3/5 (middle), and 2/3 (right) states arelisted below.dDFT calculation of hybridized band structures of 4∘ tMoSe2 with andwithout D. e Evolution of charge gaps with D for ν = 1/2 (blue solid triangle) and 3/5(red open circle) states. The inset shows typical temperature-dependent Rxx of theν = 3/5 state with varying D. f 2D map of Rxx as a function of filling factor v andtemperature T at VBG = 80 V and B =0 T. g Temperature-dependent Rxx measuredfor B =0 T (hollow symbols, upper) and 14 T (solid symbols, lower) at VBG = 90 V,respectively. ν = 1/2, red triangle (left axis); ν = 2/3, red square (left axis); ν = 1, bluecircle (right axis).Article https://doi.org/10.1038/s41467-025-59365-2Nature Communications |         (2025) 16:4058 3www.nature.com/naturecommunicationsof the region in the accessibleB−D range for the ν = 2/3 state. The ν = 1/2 state behaves similarly. We show in the Supplemental Material thatthe behavior of the two phases is consistent with our mean-field ana-lysis (see Extended Data Fig. 8). Within the insulating regime, Fig. 3cdisplays dV/dI as a function of IDC for the ν = 1/2 state at various tem-peratures. The sharp peak in dV/dI indicates a nonlinear transport atlow temperatures, from which the thermal melting can be seenthrough the collapse of the peak. The insulating states at ν = 1/2, 2/3and 3/5 can be melted thermally at T ≈ 5 K as indicated by thetemperature-dependent dV/dI curves (see Extended Data Fig. 9).Besides thermal melting, through tuning other parameters, the GWCscan alsomelt to ametallic phase at base temperature in the largeD andsmall B region.In the following, we focus on the quantum melting transitiontriggered by decreasing the magnetic field as indicated by the dashedarrow between Fig. 3a and b. We show the extracted charge gaps atν = 1/2 and 2/3 for different applied magnetic fields in Fig. 3b. As B isdecreased, the charge gap closes and a metallic state emerges.Accordingly, the dV/dI peak vanishes as shown in Fig. 3d. When D isdecreased or the electron density deviates from ν = 1/2, the nonlineartransport behavior also nearly disappears (see Extended Data Fig. 10).The correlated states at ν = 2/3 and ν = 3/5 show similar characteristics(see Extended Data Fig. 11). Therefore, our data indicates that theGWCs transit into a liquid phase due to quantum melting viadecreasing B, increasing D ormoving away from densities at fractionalfillings.We further analyze the temperature-dependent behavior of Rxxin the magnetic field-driven quantum phase transitions shown inFig. 3e and f. We collapse the Rxx curves by scaling with the criticalresistance Rc(T) of the critical magnetic field (Bc = 0 T), by the formRxx(T) = Rc(T)f(T/T0(δB))52, with T0(δB) ~ ∣δB∣zν and δB = B − Bc. Thefitting parameter T0 turns out to be comparable to the magnitude ofthe charge gap. All the data points for Rxx(T)/Rc(T) against T/T0 col-lapse well onto one curve, with a critical exponent of zν = 1.34 ± 0.02and 1.31 ± 0.03 for ν = 1/2 and 2/3 states, respectively. The scalingbehavior at ν = 3/5 state is comparable (see Extended Data Fig. 12). Itis noted that a similar power law with an exponent ~ 1.6 was reportedfor the scaling of a carrier-density-drivenMIT in silicon-based 2DES53.Phase transition of ν= 1 stateWe next investigate the phase transition of ν = 1 state. Figure 4a showsthe temperature dependent Rxx(T) of ν = 1 state at different B. WhenB < 13 T, the curves indicate metallic behavior (dRxx/dT >0) below atemperature Tmax, while above Tmax the behavior turns insulating-like(dRxx/dT <0), resulting in a resistivity maximum Rmax at Tmax. Such apronounced Rmax has been observed in 2DES38, heavy fermionsystems54, and charge-transfer organic salts55, in which the essentialmechanism of transport relies on thermal destruction of coherentquasi-particles due to strong inelastic electron-electron scattering. AtB =0 T, the Fermi-liquid behavior is restricted to a very limited range,T≪Tmax≪TF, where Tmax is the coherence temperature and TF is theFermi temperature. As the temperature increases, the electron meanfree path becomes comparable to or smaller than the moiré wave-length, leading to incoherent transport. When the electron spin istaken into account, the coherent quasiparticles can also be destroyedby adding a large enough Zeeman energy EZ to open a small band gapFig. 2 | Magnetic and displacement field tuning of generalizedWigner crystals.a Rxx as a function ofD and ν under B = 0, 3, 6, 9, 1, 2, and 14T at 1.5 K (fromdown toup). b Temperature dependence of Rxx under different B for ν = 1/2 (upper penal)and 2/3 (lower penal) states. c Charge gap evolution with B for ν = 2/3 (black), 3/5(red) and 1/2 (blue) states. The inset shows the variation of g-factor with D. Errorbars reflect the uncertainty in determining the charge gaps. d The schematic of thetransition for generalizedWigner crystal states in amagneticfield. e ν −B resistancemap of Rxx at 1.5 K and VBG = 90V. The black dotted lines label the dominantsequence in the Landau fan projecting to the band edge of tMoSe2. The whitedashed lines indicate the emergent correlated states.Article https://doi.org/10.1038/s41467-025-59365-2Nature Communications |         (2025) 16:4058 4www.nature.com/naturecommunicationsin theminibandwith abandwidthofW0 (gμBB +W0 ≥W *,W * representsthe bandwidth of metallic phase at the critical point of MITs). This is inline with our experimental observations that Tmax decreases but Rmaxincreases with magnetic field. Thus, we argue that Tmax is the coher-ence temperature beyond which incoherent transport sets in. Fig-ure 4d displays a proposed phase diagram for ν = 1 state. On themetallic side of the diagram, resistive maxima at the Brinkman-Ricetemperature TBR =Tmax signal the destruction of resilient quasi-particles and the crossover to an incoherent transport regime56.Next, we perform a scaling analysis using δR(T) = δRmaxf ðT=TmaxÞ,where δR(T) =R(T) − R0 and δRmax =Rmax � R0. We assume that theresistance follows the formulaR(T) = R0 + δR(T). Here,R0 is the residualresistivity, and δR(T) is the temperature-dependent resistance domi-nated by inelastic electron-electron scattering. As shown in Fig. 4b, thedata points over a wide B range collapse onto a single curve. Both Tmaxand δRmax show a power-law dependence on the reduced magneticfield [(B − Bc)/Bc] with an exponent of 0.60 and 0.76 (Bc = 13.5 T) asshown in Fig. 4c. Similar values are found for 2DES when scaling withcharge density38. Besides tuning the magnetic field, a MIT with perfectscaling behavior is also found when altering the density near ν = 1 (seeExtended Data Fig. 13). The Rxx(T) curves for ν = 1 state change fromquadratic to linear behavior as D decreases despite the absence of aMIT (see Extended Data Fig. 14), implying that the system isapproaching the critical point of a quantum phase transition.The physics of the ν = 1 state can also be interpreted in terms of aPomeranchuk effect describing a transition from a low-entropyelectronic liquid to a high-entropy correlated state57,58. Figure4e showsthe dual-gate maps of Rxx at different temperatures. In marked con-trast to the gradual disappearance of fractional filling insulators, theresistance of the ν = 1 state initially increases up to ~ 30K and subse-quently attenuates (see Extended Data Fig. 15).In conclusion, our observations suggest that a continuous quan-tum phase transition can be achieved in generalized Wigner crystalstates as well as the Mott state in tMoSe2 by carefully tuning a multi-parameter space consisting of magnetic field, carrier density, anddisplacement field. Our system, which hosts both Wigner and Mottstates in one single material, can serve as an ideal platform to con-tinuously tune local and long-range Coulomb interactions. The richphenomenology combined with multiple degrees of experimentalcontrol in tMoSe2 would contribute to unraveling novel states ofmatter andprovide further insights into the quantumphase transitionsbetween ordered and disordered correlated states.MethodsSample fabricationThe tMoSe2 devices were fabricated using the pick-up transfer59. Bothmonolayer MoSe2 and h-BN flakes were mechanically exfoliated ontoSiO2/Si substrates. Then the monolayer MoSe2 flake was cut into twopieces with an AFM tip. All stacks were assembled utilizing a poly-propylene carbonate (PPC)/polydimethylsiloxane (PDMS) stamp on aglass slide26,39. For the subsequentmetallization process, the PPC/hBN/tMoSe2 stack was flipped and placed on another SiO2/Si substrate withQuantum meltingc481216dV/dI(k�)IDC (nA)-100 -50 0 50 100D = 0.20 V/nm ��= 1/2B = 8 T 1.69T (K)aD (V/nm)B (T)2468101214Metallic phaseMetallic phaseGWC0.00 0.20 0.40 0.60� = 2/3 T = 1.5 K b0 0.5 1.0 1.5 2.036912B(T)Gap (K)� = 1/2 � = 2/3GeneralizedWignerCrystalddV/dI(k�)IDC (nA)-100 -50 0 50061218D = 0.20 V/nm � = 1/2T = 1.5 K 010B (T)100e0 20 400.20.40.60.81.2Rxx(k�)Temperature (K)D = 0.65 V/nm� = 1/21.0014B (T)12345T/T0R/Rc100 101 102|B – Bc| (T)1101T0 (K)� = 1.34 ± 0.02 f0.40.60.81.0Rxx(k�)D = 0.57 V/nm� = 2/30 20 40Temperature (K)014B (T)123100 101 102T/T0R/Rc� = 1.31 ± 0.03T0 (K)1101|B – Bc| (T)Fig. 3 |Melting transitions of generalizedWigner crystal states. a Phase diagramin B − D space for ν = 2/3 state at T = 1.5 K. GWC stands for generalized Wignercrystal. b Evolution of charge gap with B for ν = 1/2 (D =0.65 V/nm) and ν = 2/3(D =0.57 V/nm) states. The yellow shaded region represents the metallic phase.Error bars reflect the uncertainty in determining the charge gaps. c dV/dI as afunction of IDC for ν = 1/2 state with different temperatures under B = 8 T andD =0.20 V/nm.d dV/dI as a functionof IDC for ν = 1/2 statewith variedBunder T = 1.5K and D =0.20 V/nm. e Temperature dependence of Rxx(T) under varied B for ν = 1/2 state (left) and the corresponding scaling plot of the normalized resistivity Rxx(T)/Rc versus T/T0 (right). The inset shows the corresponding T0 vs ∣B − Bc∣. f Scalinganalysis for ν = 2/3 state. The determination of the scaling parameter T0, criticalmagnetic field Bc, and critical resistance Rc are discussed in the main text. The D-value in (c–f) is specially selected at each fractional filling to ensure the observationof melting transitions.Article https://doi.org/10.1038/s41467-025-59365-2Nature Communications |         (2025) 16:4058 5www.nature.com/naturecommunicationstMoSe2 as the top layer. A thin layer of h-BN flake (5–8 nm) was pat-terned into a Hall bar geometry by CHF3/O2 etching, picked up with anew PPC/PDMS holder, dropped onto the surface of tMoSe2, andannealed in ultrahigh vacuum. Bi/Au (6/10 nm) metal layer wasdeposited on tMoSe2 across the pre-patterned h-BN using electron-beam lithography and electron-beam evaporation to form the metal/semiconductor contacts43. Another h-BN flake (20–30nm) was pickedup and released on the as-deposited Bi/Au electrode. Finally, electron-beam lithography and evaporation were performed again to deposit aCr/Pd/Au (5/15/100 nm) metal layer to connect the Bi/Au electrodesand simultaneously define the top gate of the Hall bar channel. Thetechnical details of device fabrication herein will be reportedelsewhere.Twist angle determinationOptical SHG and atomic force microscopy were used to roughlymeasure the twist angle θ between the top and bottom MoSe2. Thevalue of θ is further confirmed with the half filling densityns = 8(1� cosθ)/ffiffiffi3pa2 of the moiré superlattices26, where a =0.3288nm is the in-plane lattice constant of H phase MoSe2. In detail,ns ~ 6.0 × 1012 cm−2 can be extracted from the fan diagram, matchingwell with the twist angle extracted from SHG.Transport measurementsElectrical transport measurements were carried out in a dilutionrefrigerator with a base temperature of 1.5 K and amaximummagneticfield of 14 T. All the data in this work were obtained using the standardlow-frequency lock-in technique at an excitation frequency of 17.777Hz with an a.c. current of 20 nA. The four-terminal resistance wasacquired by recording the source-drain current and the four-probevoltage concurrently with two lock-in amplifiers.Data availabilityThe data that support the findings of this study are available from thecorresponding authors upon request.References1. Imada, M., Fujimori, A. & Tokura, Y. Metal-insulator transitions. Rev.Mod. 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Science 342, 614–617 (2013).Article https://doi.org/10.1038/s41467-025-59365-2Nature Communications |         (2025) 16:4058 7www.nature.com/naturecommunicationsAcknowledgementsL.W. acknowledges the National Key Projects for Research and Devel-opment of China (Grant Nos. 2022YFA1204700 and 2021YFA1400400),Program for Innovative Talents and Entrepreneur in Jiangsu (GrantNo.JSSCTD202101), Natural Science Foundation of Jiangsu Province(Grant Nos. BK20220066 and BK20233001), and Nanjing UniversityInternational Research Seed Fund. G.Y. acknowledges National KeyProjects for Research and Development of China (Grant Nos.2024YFB3715400) and the National Natural Science Foundation ofChina (No. 11974169). H.W. acknowledges support from the NationalNatural Science Foundation of China (Grant No. 61804117), Natural Sci-ence Foundation of Shaanxi Province (Grant No. 2022JM-364), andGuangdong Basic and Applied Basic Research Foundation (Grant No.2022A1515111075). K.W. and T.T. acknowledge support from the JSPSKAKENHI (Grant Nos. 21H05233 and 23H02052) and World PremierInternational Research Center Initiative (WPI), MEXT, Japan. D.A.R. andY.H. acknowledge support from the University of Wisconsin-Madison,Office of the ViceChancellor for Research andGraduate Education, withfunding from the Wisconsin Alumni Research Foundation.Author contributionsL.W. conceived and designed the experiment. Q.J.Z., Q.Z., H.W., andG.Y. fabricated the samples. Q.J.Z. and H.W. performed the transportmeasurements. L.W., H.W., and Q.J.Z. analyzed the data. Y.H. and D.A.R.grew the MoSe2 crystal. K.W. and T.T. grew the h-BN crystal. L.X. andQ.X. performed the density functional theory calculation. A.R., D.M.K.,X.C., and A.F. performed the mean field theory calculation. L.W., H.W.,and Q.J.Z. wrote the manuscript with input from all the authors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-59365-2.Correspondence and requests for materials should be addressed toHaolin Wang, Angel Rubio, Geliang Yu or Lei Wang.Peer review information Nature Communications thanks the anon-ymous reviewer(s) for their contribution to thepeer reviewof thiswork. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-025-59365-2Nature Communications |         (2025) 16:4058 8https://doi.org/10.1038/s41467-025-59365-2http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Quantum melting of generalized electron crystal in twisted bilayer MoSe2 Results and discussion Correlated states at integer and fractional fillings Magnetic and displacement field effects Quantum melting transitions Phase transition of ν = 1 state Methods Sample fabrication Twist angle determination Transport measurements Data availability References Acknowledgements Author contributions Competing interests Additional information