Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices


Moiré superlattices can be used to engineer strongly correlated electronic states in two-dimensional van der Waals heterostructures, as recently demonstrated in the correlated insulating and superconducting states observed in magic-angle twisted-bilayer graphene and ABC trilayer graphene/boron nitride moiré superlattices1,2,3,4. Transition metal dichalcogenide moiré heterostructures provide another model system for the study of correlated quantum phenomena5 because of their strong light–matter interactions and large spin–orbit coupling. However, experimental observation of correlated insulating states in this system is challenging with traditional transport techniques. Here we report the optical detection of strongly correlated phases in semiconducting WSe2/WS2 moiré superlattices. We use a sensitive optical detection technique and reveal a Mott insulator state at one hole per superlattice site and surprising insulating phases at 1/3 and 2/3 filling of the superlattice, which we assign to generalized Wigner crystallization on the underlying lattice6,7,8,9,10,11. Furthermore, the spin–valley optical selection rules12,13,14 of transition metal dichalcogenide heterostructures allow us to optically create and investigate low-energy excited spin states in the Mott insulator. We measure a very long spin relaxation lifetime of many microseconds in the Mott insulating state, orders of magnitude longer than that of charge excitations. Our studies highlight the value of using moiré superlattices beyond graphene to explore correlated physics.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Optically detected resistance and capacitance technique in a WSe2/WS2 superlattice.
Fig. 2: Doping-dependent resistance and capacitance probed by ODRC.
Fig. 3: Temperature dependence of Mott and generalized Wigner crystal states.
Fig. 4: Optical investigation of low-energy spin excitation dynamics of a WSe2/WS2 Mott insulator.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    CAS  ADS  Article  Google Scholar 

  2. 2.

    Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    CAS  ADS  Article  Google Scholar 

  3. 3.

    Chen, G. et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys. 15, 237–241 (2019).

    CAS  Article  Google Scholar 

  4. 4.

    Chen, G. et al. Signatures of tunable superconductivity in a trilayer graphene moiré superlattice. Nature 572, 215–219 (2019).

    CAS  Article  Google Scholar 

  5. 5.

    Wu, F., Lovorn, T., Tutuc, E. & MacDonald, A. H. Hubbard model physics in transition metal dichalcogenide moire bands. Phys. Rev. Lett. 121, 026402 (2018).

    CAS  ADS  Article  Google Scholar 

  6. 6.

    Wigner, E. On the interaction of electrons in metals. Phys. Rev. 46, 1002–1011 (1934).

    CAS  ADS  Article  Google Scholar 

  7. 7.

    Hubbard, J. Generalized Wigner lattices in one dimension and some applications to tetracyanoquinodimethane (TCNQ) salts. Phys. Rev. B 17, 494–505 (1978).

    CAS  ADS  Article  Google Scholar 

  8. 8.

    Wu, C., Bergman, D., Balents, L. & Das Sarma, S. Flat bands and Wigner crystallization in the honeycomb optical lattice. Phys. Rev. Lett. 99, 070401 (2007).

    ADS  Article  Google Scholar 

  9. 9.

    Hiraki, K. & Kanoda, K. Wigner crystal type of charge ordering in an organic conductor with a quarter-filled band: (D1-DCNQI)2Ag. Phys. Rev. Lett. 80, 4737–4740 (1998).

    CAS  ADS  Article  Google Scholar 

  10. 10.

    Padhi, B., Setty, C. & Phillips, P. W. Doped twisted bilayer graphene near magic angles: proximity to Wigner crystallization, not Mott insulation. Nano Lett. 18, 6175–6180 (2018).

    CAS  ADS  Article  Google Scholar 

  11. 11.

    Padhi, B. & Phillips, P. W. Pressure-induced metal-insulator transition in twisted bilayer graphene. Phys. Rev. B 99, 205141 (2019).

    CAS  ADS  Article  Google Scholar 

  12. 12.

    Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polarization in monolayer MoS2 by optical helicity. Nat. Nanotechnol. 7, 494–498 (2012).

    CAS  ADS  Article  Google Scholar 

  13. 13.

    Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).

    ADS  Article  Google Scholar 

  14. 14.

    Cao, T. et al. Valley-selective circular dichroism of monolayer molybdenum disulphide. Nat. Commun. 3, 887 (2012).

    ADS  Article  Google Scholar 

  15. 15.

    Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in trilayer graphene/boron nitride moire superlattice. Preprint at (2019).

  16. 16.

    Kadantsev, E. S. & Hawrylak, P. Electronic structure of a single MoS2 monolayer. Solid State Commun. 152, 909–913 (2012).

    CAS  ADS  Article  Google Scholar 

  17. 17.

    Fallahazad, B. et al. Shubnikov–de Haas oscillations of high-mobility holes in monolayer and bilayer WSe2 Landau level degeneracy, effective mass, and negative compressibility. Phys. Rev. Lett. 116, 086601 (2016).

    ADS  Article  Google Scholar 

  18. 18.

    Roch, J. G. et al. Spin-polarized electrons in monolayer MoS2. Nat. Nanotechnol. 14, 432–436 (2019).

    CAS  ADS  Article  Google Scholar 

  19. 19.

    Back, P. et al. Giant paramagnetism-induced valley polarization of electrons in charge-tunable monolayer MoSe2. Phys. Rev. Lett. 118, 237404 (2017).

    ADS  Article  Google Scholar 

  20. 20.

    Splendiani, A. et al. Emerging photoluminescence in monolayer MoS2. Nano Lett. 10, 1271–1275 (2010).

    CAS  ADS  Article  Google Scholar 

  21. 21.

    Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).

    ADS  Article  Google Scholar 

  22. 22.

    Mott, N. F. The basis of the electron theory of metals, with special reference to the transition metals. Proc. Phys. Soc. A 62, 416–422 (1949).

    ADS  Article  Google Scholar 

  23. 23.

    Imada, M., Fujimori, A. & Tokura, Y. Metal-insulator transitions. Rev. Mod. Phys. 70, 1039–1263 (1998).

    CAS  ADS  Article  Google Scholar 

  24. 24.

    Allain, A., Kang, J., Banerjee, K. & Kis, A. Electrical contacts to two-dimensional semiconductors. Nat. Mater. 14, 1195–1205 (2015).

    CAS  ADS  Article  Google Scholar 

  25. 25.

    Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019); correction 569, E7 (2019).

    CAS  ADS  Article  Google Scholar 

  26. 26.

    Zhang, Y., Yuan, N. F. Q. & Fu, L. Moiré quantum chemistry: charge transfer in transition metal dichalcogenide superlattices. Preprint at (2019).

  27. 27.

    Lenarčič, Z. & Prelovšek, P. Ultrafast charge recombination in a photoexcited Mott–Hubbard insulator. Phys. Rev. Lett. 111, 016401 (2013).

    ADS  Article  Google Scholar 

  28. 28.

    Okamoto, H. et al. Photoinduced transition from Mott insulator to metal in the undoped cuprates. Phys. Rev. B 83, 125102 (2011).

    ADS  Article  Google Scholar 

  29. 29.

    Giannetti, C. et al. Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach. Adv. Phys. 65, 58–238 (2016).

    CAS  ADS  Article  Google Scholar 

  30. 30.

    Kim, J. et al. Observation of ultralong valley lifetime in WSe2/MoS2 heterostructures. Sci. Adv. 3, e1700518 (2017).

    ADS  Article  Google Scholar 

  31. 31.

    Jin, C. et al. Imaging of pure spin–valley diffusion current in WS2/WSe2 heterostructures. Science 360, 893–896 (2018).

    CAS  ADS  Article  Google Scholar 

  32. 32.

    Law, K. T. & Lee, P. A. 1T-TaS2 as a quantum spin liquid. Proc. Natl Acad. Sci. USA 114, 6996–7000 (2017).

    CAS  ADS  Article  Google Scholar 

  33. 33.

    Grover, T., Trivedi, N., Senthil, T. & Lee, P. A. Weak Mott insulators on the triangular lattice: Possibility of a gapless nematic quantum spin liquid. Phys. Rev. B 81, 245121 (2010).

    ADS  Article  Google Scholar 

  34. 34.

    Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    CAS  ADS  Article  Google Scholar 

  35. 35.

    Kumar, N. et al. Second harmonic microscopy of monolayer MoS2. Phys. Rev. B 87, 161403 (2013).

    ADS  Article  Google Scholar 

  36. 36.

    Li, Y. et al. Probing symmetry properties of few-layer MoS2 and h-BN by optical second-harmonic generation. Nano Lett. 13, 3329–3333 (2013).

    CAS  ADS  Article  Google Scholar 

Download references


We thank S. Li for discussions, S. Wang for help with device fabrication, and C. Stansbury and C. Wang for assistance with figure design. This work was supported primarily by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under contract number DE-AC02-05-CH11231 (van der Waals heterostructures programme, KCWF16). The device fabrication was also supported by the US Army Research Office under MURI award W911NF-17-1-0312. E.C.R. acknowledges support from the Department of Defense through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program. C.J. acknowledges support from a Kavli Postdoctoral Fellowship. S.T. acknowledges support from NSF DMR-1552220 and 1838443.

Author information




F.W. conceived the research. E.C.R., D.W. and C.J. carried out optical measurements. D.W., E.C.R., C.J. and F.W. performed data analysis. E.C.R., D.W., B.G., X.W., M.I.B.U., S.Z., W.Z., Z.Z., J.D.C., M.C. and A.Z. contributed to the fabrication of van der Waals heterostructures. K.Y., M.B. and S.T. grew WSe2 and WS2 crystals. K.W. and T.T. grew hBN crystals. All authors discussed the results and wrote the manuscript.

Corresponding author

Correspondence to Feng Wang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Alexander Tartakovskii and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 WSe2 A exciton gate behaviour.

a, Reflection contrast spectra for the lowest-energy WSe2 A exciton resonance in region 2 of device D1 when the local top-gate voltage Vtop is tuned from 0.5 V to –3.5 V. Region 2 is not affected when the hole concentration is tuned in region 1 by Vtop. b, Reflection contrast spectra for the WSe2 A exciton in region 2 when the global back gate is tuned from −0.95 V to −1.05 V. The inset shows a zoomed-in view of the exciton peak. The spectral change is monotonic and approximately linear with carrier concentration.

Extended Data Fig. 2

ODRC signal measured at very low frequencies for a range of modulation voltages. Vmod, modulation voltage.

Extended Data Fig. 3 Calibration of hBN dielectric constant.

a, MoSe2 A exciton peak intensity measured while tuning the voltages of the top graphite gate and back Si gate. b, The extracted charge-neutral points (CNP, dots) for each Si back gate, corresponding to the top graphite gate voltages that bring the system to zero net charge. The black line is a linear fit to the data, from which the relative gate efficiency is determined.

Extended Data Fig. 4 Determination of WSe2 and WS2 flake alignment.

Polarization-dependent SHG signal on monolayer WSe2 (red circles) and WS2 (black circles) regions of device D1 and corresponding fittings (red and black curves, respectively).

Extended Data Fig. 5 ODRC signal for other aligned WSe2/WS2 heterostructures.

a, b, ODRC signal at low (grey) and high (black) frequency from charge-neutral to moderate hole doping in devices D2 (a) and D3 (b). The dashed lines are guides to the eye at hole concentrations of n = 0 (purple), n = n0/3 (orange), n = 2n0/3 (green) and n = n0 (blue).

Extended Data Fig. 6 ODRC signal for a large-twist-angle WSe2/WS2 heterostructure.

a, Normalized ΔOC for a large-twist-angle heterostructure (D4, blue) and an aligned heterostructure (D1, black). The misaligned heterostructure does not show any insulating features. b, The frequency dependence of the large-twist-angle heterostructure signal shows a characteristic RC circuit fall-off with increasing frequency.

Supplementary information

Supplementary Information

This file contains the Effective AC Circuit Model.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Regan, E.C., Wang, D., Jin, C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.