An exciton crystal in a moiré excitonic insulator

Nature Physics (2026)Cite this article Strong Coulomb interactions can drive electrons to crystallize into a Wigner lattice. Achieving the bosonic analogue—a crystal of excitons—has remained challenging owing to their short lifetimes and weaker interactions. Here we report the observation of a thermodynamically stable exciton crystal in an excitonic insulator coupled to a moiré potential. Using an electron–hole bilayer composed of a monolayer MoSe2 and a WS2/WSe2 moiré superlattice, we constructed a tunable extended Bose–Hubbard system with electrical control over exciton and charge doping in thermal equilibrium. Optical spectroscopy revealed spontaneous crystallization of long-lived excitons at one exciton filling per three moiré sites, manifested as strong Umklapp scattering peaks. Exciton transport measurements further showed a pronounced exciton resistance peak at the same filling. When doped away from net charge neutrality, this moiré electron–hole bilayer can host correlated insulating phases in which dipolar excitonic insulators form on top of the background of a hole Mott insulator or generalized Wigner crystals. These findings establish moiré electron–hole bilayers as a versatile platform for realizing correlated crystalline phases of bosons and fermions.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutThe data that support the findings of this study are available from the corresponding author upon request. Source data are provided with this paper.Wigner, E. 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The van der Waals heterostructure fabrication and electrical characterization were supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under contract no. DE-AC02-05-CH11231 (van der Waals heterostructures program; KCWF16 to F.W.). The optical–electrical four-terminal exciton transport was supported by the AFOSR award (FA9550-23-1-0246 to F.W.). K.W. and T.T. acknowledge support from the JSPS KAKENHI (21H05233 and 23H02052) and World Premier International Research Center Initiative, MEXT.These authors contributed equally: Ruishi Qi, Qize Li.Department of Physics, University of California, Berkeley, Berkeley, CA, USARuishi Qi, Qize Li, Haleem Kim, Jiahui Nie, Zuocheng Zhang, Ruichen Xia, Zhiyuan Cui, Jianghan Xiao, Michael F. Crommie & Feng WangMaterials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USARuishi Qi, Haleem Kim, Jiahui Nie, Jianghan Xiao, Michael F. Crommie & Feng WangGraduate Group in Applied Science and Technology, University of California, Berkeley, Berkeley, CA, USAQize Li, Jiahui Nie & Jianghan XiaoResearch Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, JapanTakashi TaniguchiResearch Center for Functional Materials, National Institute for Materials Science, Tsukuba, JapanKenji WatanabeKavli Energy NanoScience Institute, University of California, Berkeley and Lawrence Berkeley National Laboratory, Berkeley, CA, USAFeng WangSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarF.W. and R.Q. conceived the research. Q.L., R.Q., J.N., R.X., Z.C. and J.X. fabricated the devices. R.Q., Q.L. and H.K. performed the optical measurements. R.Q. and Z.Z. performed the transport measurements. R.Q., Q.L., M.F.C. and F.W. analysed the data. K.W. and T.T. grew hBN crystals. All authors discussed the results and wrote the paper.Correspondence to Feng Wang.The authors declare no competing interests.Nature Physics thanks Shun Feng and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.a, Schematic band alignment of the WS2/WSe2/hBN/MoSe2 heterostructure. The active conduction and valence bands lie in MoSe2 and WSe2 respectively. b, Gate-dependent reflection spectra at \({V}_{{\rm{B}}}=0.7\,{\rm{V}}\) (pink horizontal line in c). Upon electron doping, the MoSe2 X0 peak loses oscillator strength while the MoSe2 X− peak appears. Upon hole doping, the WSe2 main moiré exciton peak loses oscillator strength while a WSe2 X+-like peak emerges. WS2 moiré exciton peaks remain nearly constant (with small wavelength shifts at insulating states), and there is no trion-like peak. c–e, 2D color plots of the reflection contrast at MoSe2 X0 resonance (c), WSe2 main moiré exciton peak (d), and WS2 main moiré exciton peak (e). Upon electron doping, the MoSe2 X0 has strong contrast change. Upon hole doping, the WSe2 moiré exciton peak has strong contrast change. The WS2 peak intensity remains nearly constant.a, Interlayer tunnelling current for device D1 as a function of \({V}_{{\rm{G}}}\) and \({V}_{{\rm{B}}}\) at antisymmetric gating \({V}_{{\rm{BG}}}/2-{V}_{{\rm{TG}}}/2=2.5\,{\rm{V}}\) (electric field 0.38 V/nm). Fitting the tunnelling current along the charge neutral line (blue dashed line) as a function of \({V}_{{\rm{B}}}\) gives an increase rate of 14 nA/V, indicating a tunnelling resistance of ~108 Ω. b, Interlayer tunnelling current for device D2 at antisymmetric gating \({V}_{{\rm{BG}}}/2-{V}_{{\rm{TG}}}/2=3.5\,{\rm{V}}\) (electric field 0.41 V/nm). A slightly thicker hBN barrier (6-layer hBN for D2, 5-layer hBN for D1) leads to an even larger tunnelling resistance of ~109 Ω.a, Optical microscopy image of device D2. b, c, Reflection contrast intensity at the MoSe2 main exciton peak (1.637 eV) and WSe2 main moiré exciton peak (1.671 eV), respectively, as functions of \({V}_{{\rm{G}}}\) and \({V}_{{\rm{B}}}\). The vertical electric field is fixed at 0.41 V/nm. The general phase diagram is consistent with device D1 shown in Fig. 1. d, Reflection spectrum linecut along net charge neutrality as a function of \({V}_{{\rm{B}}}\), showing the emergence of a satellite peak (Umklapp scattering) at 1/3 exciton filling. e, Blue, reflection spectrum at 1/3 exciton filling (\({n}_{{\rm{e}}}={n}_{{\rm{h}}}={n}_{0}/3\)). Magenta, reflection spectrum when the system is at similar doping density but doped exclusively with electrons (\({n}_{{\rm{e}}}={n}_{0}/3\) and \({n}_{{\rm{h}}}=0\)).a, Gate-dependent reflection spectra at constant \({V}_{{\rm{B}}}=0.547\,{\rm{V}}\) (device D2). This voltage cuts across 1/3 exciton filling when \({n}_{{\rm{e}}}={n}_{{\rm{h}}}\); increasing or decreasing \({V}_{{\rm{G}}}\) introduces charge imbalance, and the Umklapp peak is quickly quenched. b, Gate-dependent reflection spectra along constant \({n}_{{\rm{e}}}={n}_{0}/3\) line. The Umklapp peak only appears at charge neutrality. c, Gate-dependent reflection spectra along constant \({n}_{{\rm{h}}}={n}_{0}/3\) line. d, Reflection spectra along the charge neutrality line. The Umklapp peak only appears near 1/3 exciton doping, not at other general filling factors. e, 2D color plot of the Umklapp peak intensity, showing a hot spot concentrated at \({n}_{{\rm{e}}}={n}_{{\rm{h}}}={n}_{0}/3\). For each spectrum, the main X0 peak is fitted to a Fano line shape and subtracted. The resulting intensity at the Umklapp peak energy (1.649 eV) is used as the Umklapp intensity. Yellow dotted lines correspond to the voltage traces in a–d.a–d, Reflection spectra along the net charge neutrality line for different temperatures, as a function of filling factor \({n}_{{\rm{x}}}/{n}_{0}\) (device D2). The Umklapp peak at 1/3 filling is well defined at low temperatures, becomes weaker at 16 K, and eventually disappears at 20 K. e, Evolution of the reflection spectrum at \({n}_{{\rm{x}}}/{n}_{0}=1/3\) at various temperatures. The spectra at low temperatures all collapse together and clearly show the Umklapp peak, suggesting a well-defined exciton crystal. At higher temperatures it weakens, and becomes completely featureless at 20 K. f, The spectrum intensity at 1.649 eV (black triangle in e), as a function of exciton filling factor and temperature. The Umklapp peak appears only at 1/3 filling, and gradually diminishes after ~15 K.a, Raw reflection contrast spectrum as a function of electron doping density when the hole layer is undoped (device D2). Only the main X0 peak is visible. b, Energy derivative of the spectra shown in a. Still only the main X0 peak is visible. c, Density derivative of the spectra shown in b. The Umklapp peak appears below density \(\sim 3\times {10}^{11}\,{{\rm{cm}}}^{-2}\), consistent with spontaneous formation of electron Wigner crystals when the density is sufficiently low. The double derivative suppresses the slow-decaying tail of the main peak, revealing the weak Umklapp peak. d, Raw reflection contrast spectrum as a function of exciton doping density along net charge neutrality line. The Umklapp scattering peak at 1/3 exciton filling, although weak compared to the main peak, is readily visible without taking any derivative. e, Energy derivative of the spectra shown in d. The Umklapp peak is very clear. f, Density derivative of the spectra shown in e. The Umklapp peak in d–f is substantially stronger than the electron Wigner crystal case, suggestive of a more ordered crystal structure. This can be explained by the presence of the moiré potential defining a common crystal orientation. In contrast, the electron Wigner crystal in monolayer MoSe2 does not have an intrinsically preferred orientation, which is usually determined by local defects or strain and therefore more vulnerable to sample inhomogeneities.a, Circuit diagram of the resistance measurement. The a.c. drive voltage is distributed on the two MoSe2 contacts (\({V}_{{\rm{L}}}=\alpha \Delta V\) and \({V}_{{\rm{R}}}=-\left(1-\alpha \right)\Delta V\)), with portion \(\alpha\) on the left. It excites an exciton current in the EI, which is measured as \({I}_{{\rm{drive}}}\). The potential distribution is then optically readout. b, Density dependence of the reflection contrast spectrum. A monochromatic laser (gray line) reflected back from the device is used to probe the local potential distribution. c, d, Measured a.c. optical response at two representative doping conditions. For exciton filling \({n}_{{\rm{x}}}/{n}_{0}=1/3\) (c), the zero crossing point of the optical signal depends strongly on the position, indicating a large potential gradient due to the high resistance in the exciton crystal state. For exciton filling 0.44 (d), the resistance is much smaller. e, \((\alpha ,x)\) relation by tracing the zero crossing point of the a.c. optical signal.Empty circles, optically measured \({R}_{{\rm{x}}}^{4{\rm{t}}}\) as a function of temperature at exciton filling \({n}_{{\rm{x}}}/{n}_{0}=1/3\). Solid curve, fitting result using a thermal activation function \({R}_{0}\exp ({T}_{0}/T)\).Source data for Fig. 1.Source data for Fig. 2.Source data for Fig. 3.Source data for Fig. 4.Reprints and permissionsQi, R., Li, Q., Kim, H. et al. An exciton crystal in a moiré excitonic insulator. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03184-9Download citationReceived: 31 August 2025Accepted: 15 January 2026Published: 18 February 2026Version of record: 18 February 2026DOI: https://doi.org/10.1038/s41567-026-03184-9Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative