Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Stripe phases in WSe2/WS2 moiré superlattices


Stripe phases, in which the rotational symmetry of charge density is spontaneously broken, occur in many strongly correlated systems with competing interactions1,2,3,4,5,6,7,8,9,10,11. However, identifying and studying such stripe phases remains challenging. Here we uncover stripe phases in WSe2/WS2 moiré superlattices by combining optical anisotropy and electronic compressibility measurements. We find strong electronic anisotropy over a large doping range peaked at 1/2 filling of the moiré superlattice. The 1/2 state is incompressible and assigned to an insulating stripe crystal phase. Wide-field imaging reveals domain configurations with a preferential alignment along the high-symmetry axes of the moiré superlattice. Away from 1/2 filling, we observe additional stripe crystals at commensurate filling 1/4, 2/5 and 3/5, and compressible electronic liquid crystal states at incommensurate fillings. Our results demonstrate that two-dimensional semiconductor moiré superlattices are a highly tunable platform from which to study the stripe phases and their interplay with other symmetry breaking ground states.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Optical detection of electronic anisotropy.
Fig. 2: Electronic anisotropy in WSe2/WS2 moiré superlattices.
Fig. 3: Temperature dependence.
Fig. 4: Stripe domains at ν = 1/2.

Similar content being viewed by others

Data availability

The data that support the findings of this study are available within the paper and its Supplementary Information. Source data are provided with this paper.


  1. Emery, V. J., Kivelson, S. A. & Tranquada, J. M. Stripe phases in high-temperature superconductors. Proc. Natl Acad. Sci. USA 96, 8814–8817 (1999).

    Article  CAS  Google Scholar 

  2. Lee, P. A., Nagaosa, N. & Wen, X. G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).

    Article  CAS  Google Scholar 

  3. Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).

    Article  CAS  Google Scholar 

  4. Stewart, G. R. Superconductivity in iron compounds. Rev. Mod. Phys. 83, 1589–1652 (2011).

    Article  CAS  Google Scholar 

  5. Koulakov, A. A., Fogler, M. M. & Shklovskii, B. I. Charge density wave in two-dimensional electron liquid in weak magnetic field. Phys. Rev. Lett. 76, 499–502 (1996).

    Article  CAS  Google Scholar 

  6. Du, R. R. et al. Strongly anisotropic transport in higher two-dimensional Landau levels. Solid State Commun. 109, 389–394 (1999).

    Article  CAS  Google Scholar 

  7. Lilly, M. P., Cooper, K. B., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Evidence for an anisotropic state of two-dimensional electrons in high Landau levels. Phys. Rev. Lett. 82, 394–397 (1999).

    Article  CAS  Google Scholar 

  8. Li, J. R. et al. A stripe phase with supersolid properties in spin-orbit-coupled Bose-Einstein condensates. Nature 543, 91–94 (2017).

    Article  CAS  Google Scholar 

  9. Cao, Y. et al. Nematicity and competing orders in superconducting magic-angle graphene. Preprint at (2020).

  10. Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).

    Article  CAS  Google Scholar 

  11. Jiang, Y. H. et al. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature 573, 91–95 (2019).

    Article  CAS  Google Scholar 

  12. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moire heterostructure. Science 367, 900–903 (2020).

    Article  CAS  Google Scholar 

  13. Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  17. Zhang, Z. M. et al. Flat bands in twisted bilayer transition metal dichalcogenides. Nat. Phys. 16, 1093–1096 (2020).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  19. Tang, Y. H. et al. Simulation of Hubbard model physics in WSe2/WS2 moire superlattices. Nature 579, 353–358 (2020).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  21. Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).

    Article  CAS  Google Scholar 

  22. Wu, F. C. & Das Sarma, S. Collective excitations of quantum anomalous Hall ferromagnets in twisted bilayer graphene. Phys. Rev. Lett. 124, 046403 (2020).

    Article  CAS  Google Scholar 

  23. Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moire heterostructure. Nature 580, 472–477 (2020).

    Article  CAS  Google Scholar 

  24. Jin, C. H. et al. Observation of moire excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019).

    Article  CAS  Google Scholar 

  25. Zhang, Y., Yuan, N. F. Q. & Fu, L. Moire quantum chemistry: charge transfer in transition metal dichalcogenide superlattices. Phys. Rev. B. 102, 201115 (2020).

    Article  CAS  Google Scholar 

  26. Xu, Y. et al. Correlated insulating states at fractional fillings of moire superlattices. Nature 587, 214–218 (2020).

    Article  CAS  Google Scholar 

  27. Jin, C. et al. Imaging and control of critical fluctuations in two-dimensional magnets. Nat. Mater. 19, 1290–1294 (2020).

    Article  CAS  Google Scholar 

  28. Fernandes, R. M. & Venderbos, J. W. F. Nematicity with a twist: rotational symmetry breaking in a moiré superlattice. Sci. Adv. 6, eaba8834 (2020).

  29. Tasaki, H. The Hubbard model—an introduction and selected rigorous results. J. Phys.-Condens Mat. 10, 4353–4378 (1998).

    Article  CAS  Google Scholar 

  30. Kivelson, S. A., Fradkin, E. & Emery, V. J. Electronic liquid-crystal phases of a doped Mott insulator. Nature 393, 550–553 (1998).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  32. Pan, H. N., Wu, F. C. & Das Sarma, S. Quantum phase diagram of a Moiré–Hubbard model. Phys. Rev. B. 102, 201104 (2020).

    Article  CAS  Google Scholar 

  33. Ashoori, R. C. et al. Single-electron capacitance spectroscopy of discrete quantum levels. Phys. Rev. Lett. 68, 3088–3091 (1992).

    Article  CAS  Google Scholar 

  34. Zibrov, A. A. et al. Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level. Nature 549, 360–364 (2017).

    Article  CAS  Google Scholar 

  35. Shi, Q. H. et al. Odd- and even-denominator fractional quantum Hall states in monolayer WSe2. Nat. Nanotechnol. 15, 569–573 (2020).

    Article  CAS  Google Scholar 

  36. Kaburagi, M. & Kanamori, J. Ground-state structure of triangular lattice gas model with up to 3rd-neighbor interactions. J. Phys. Soc. Jpn. 44, 718–727 (1978).

    Article  CAS  Google Scholar 

  37. Coppersmith, S. N., Fisher, D. S., Halperin, B. I., Lee, P. A. & Brinkman, W. F. Dislocations and the commensurate-incommensurate transition in two dimensions. Phys. Rev. Lett. 46, 549–552 (1981).

    Article  Google Scholar 

  38. Bak, P., Mukamel, D., Villain, J. & Wentowska, K. Commensurate-incommensurate transitions in rare-gas monolayers adsorbed on graphite and in layered charge-density-wave systems. Phys. Rev. B. 19, 1610–1613 (1979).

    Article  CAS  Google Scholar 

  39. Mahmoudian, S., Rademaker, L., Ralko, A., Fratini, S. & Dobrosavljevic, V. Glassy dynamics in geometrically frustrated Coulomb liquids without disorder. Phys. Rev. Lett. 115, 025701 (2015).

    Article  Google Scholar 

Download references


We thank E.-A. Kim for fruitful discussions. This work was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under award number DE-SC0019481 (growth of WSe2 crystals and optical characterization), the US Army Research Office under grant number W911NF-17-1-0605 (device fabrication), the US Office of Naval Research under award number N00014-18-1-2368 (capacitance measurements) and the Air Force Office of Scientific Research under award number FA9550-20-1-0219 (optical microscopy). The growth of hBN crystals was supported by the Elemental Strategy Initiative of MEXT, Japan and CREST (grant no. JPMJCR15F3). L.F. acknowledges support from the Simons Investigator Award from the Simons Foundation. K.F.M. acknowledges support from the David and Lucille Packard Fellowship. C.J. acknowledges support from the Kavli Postdoctoral Fellowship. Z.T. acknowledges support from the Watt W. Webb Graduate Fellowship in Nanoscience.

Author information

Authors and Affiliations



C.J. and Z.T. performed the optical experiments and analysis. T.L. and J.Z. performed the capacitance experiment and analysis. L.F. performed theoretical analysis. T.L., Z.T., Y.X., Y.T. and J.Z. fabricated the devices. S.L. and J.C.H. grew the bulk TMD crystals. K.W. and T.T. grew the bulk hBN crystals. C.J., J.S. and K.F.M. designed the scientific objectives and oversaw the project. C.J., J.S. and K.F.M. cowrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Chenhao Jin, Liang Fu, Jie Shan or Kin Fai Mak.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Materials thanks the anonymous reviewers 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.

Supplementary information

Supplementary Information

Supplementary Notes 1–9 and Figs. 1–11.

Source data

Source Data Fig. 1

Source data for penetration capacitance and PL in Fig. 1d.

Source Data Fig. 2

Source data for Fig. 2 with each panel given as a different tab.

Source Data Fig. 3

Source data for Fig. 3 with each panel given as a different tab.

Source Data Fig. 4

Source data for Fig. 4a,b,c,e with each panel given as a different tab.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jin, C., Tao, Z., Li, T. et al. Stripe phases in WSe2/WS2 moiré superlattices. Nat. Mater. 20, 940–944 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing