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.

Moiré nematic phase in twisted double bilayer graphene


Graphene moiré superlattices display electronic flat bands. At integer fillings of these flat bands, energy gaps due to strong electron–electron interactions are generally observed. However, the presence of other correlation-driven phases in twisted graphitic systems at non-integer fillings is unclear. Here, we report the existence of three-fold rotational (C3) symmetry breaking in twisted double bilayer graphene. Using spectroscopic imaging over large and uniform areas to characterize the direction and degree of C3 symmetry breaking, we find it to be prominent only at energies corresponding to the flat bands and nearly absent in the remote bands. We demonstrate that the magnitude of the rotational symmetry breaking does not depend on the degree of the heterostrain or the displacement field, being instead a manifestation of an interaction-driven electronic nematic phase. We show that the nematic phase is a primary order that arises from the normal metal state over a wide range of doping away from charge neutrality. Our modelling suggests that the nematic instability is not associated with the local scale of the graphene lattice, but is an emergent phenomenon at the scale of the moiré lattice.

Your institute does not have access to this article

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: LDOS in twisted double bilayer graphene.
Fig. 2: Broken C3 symmetry.
Fig. 3: Manifestations of long-range nematic order in TDBG.
Fig. 4: Moiré nematic order.

Data availability

All data that support the plots in this paper are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

All relevant source code is available from the corresponding author upon reasonable request.


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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Choi, Y. et al. Electronic correlations in twisted bilayer graphene near the magic angle. Nat. Phys. 15, 1174–1180 (2019).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Urgell, C., Watanabe, K., Taniguchi, T., Zhang, G. & Bachtold, A. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 20–23 (2019).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Shen, C. et al. Correlated states in twisted double bilayer graphene. Nat. Phys. 16, 520–525 (2020).

    Article  Google Scholar 

  10. Liu, X. et al. Spin-polarized correlated insulator and superconductor in twisted double bilayer graphene. Nature 583, 221–225 (2020).

    Article  ADS  Google Scholar 

  11. Cao, Y. et al. Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene. Nature (2020).

  12. He, M. et al. Tunable correlation-driven symmetry breaking in twisted double bilayer graphene. Nat. Phys. 17, 26–30 (2021).

    Article  Google Scholar 

  13. Liu, X. et al. Spectroscopy of a tunable moiré system with a correlated and topological flat band. Nat. Commun. 12, 2732 (2021).

    Article  ADS  Google Scholar 

  14. Zhang, C. et al. Visualizing delocalized correlated electronic states in twisted double bilayer graphene. Nat. Commun. 12, 2516 (2021).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  16. Lyu, B. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).

    Article  ADS  Google Scholar 

  17. Williams, R. Liquid crystals in an electric field. Nature 199, 273–274 (1963).

    Article  ADS  Google Scholar 

  18. Fradkin, E., Kivelson, S. A., Lawler, M. J. & Mackenzie, A. P. Nematic Fermi fluids in condensed matter physics. Annu. Rev. Condens. Matter Phys. 1, 153–178 (2010).

    Article  ADS  Google Scholar 

  19. Fernandes, R. M., Chubukov, A. V. & Schmalian, J. What drives nematic order in iron-based superconductors? Nat. Phys. 10, 97–104 (2014).

    Article  Google Scholar 

  20. Cao, Y. et al. Nematicity and competing orders in superconducting magic-angle graphene. Science 372, 264–271 (2021).

    Article  ADS  Google Scholar 

  21. Kerelsky, A. et al. Moiréless correlations in ABCA graphene. Proc. Natl Acad. Sci. USA 118, e2017366118 (2020).

    Article  Google Scholar 

  22. Edelberg, D., Kumar, H., Shenoy, V., Ochoa, H. & Pasupathy, A. N. Tunable strain soliton networks confine electrons in van der Waals materials. Nat. Phys. 16, 1097–1102 (2020).

    Article  Google Scholar 

  23. Haddadi, F., Wu, Q., Kruchkov, A. J. & Yazyev, O. V. Moiré flat bands in twisted double bilayer graphene. Nano Lett. 20, 2410–2415 (2020).

    Article  ADS  Google Scholar 

  24. Koshino, M. Band structure and topological properties of twisted double bilayer graphene. Phys. Rev. B 99, 235406 (2019).

    Article  ADS  Google Scholar 

  25. Samajdar, R. & Scheurer, M. S. Microscopic pairing mechanism, order parameter, and disorder sensitivity in moiré superlattices: applications to twisted double-bilayer graphene. Phys. Rev. B 102, 064501 (2020).

    Article  ADS  Google Scholar 

  26. Yankowitz, M. et al. Band structure mapping of bilayer graphene via quasiparticle scattering quasiparticle scattering. APL Mater. 2, 092503 (2014).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  28. Bi, Z., Yuan, N. F. Q. & Fu, L. Designing flat bands by strain. Phys. Rev. B 100, 035448 (2019).

    Article  ADS  Google Scholar 

  29. Scheurer, M. S. & Samajdar, R. Pairing in graphene-based moiré superlattices. Phys. Rev. Res. 2, 033062 (2020).

    Article  Google Scholar 

  30. Venderbos, J. W. F. & Fernandes, R. M. Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene. Phys. Rev. B 98, 245103 (2018).

    Article  ADS  Google Scholar 

  31. Dodaro, J. F., Kivelson, S. A., Schattner, Y., Sun, X. Q. & Wang, C. Phases of a phenomenological model of twisted bilayer graphene. Phys. Rev. B 98, 075154 (2018).

    Article  ADS  Google Scholar 

  32. Isobe, H., Yuan, N. F. Q. & Fu, L. Unconventional superconductivity and density waves In twisted bilayer graphene. Phys. Rev. X 8, 041041 (2018).

    Google Scholar 

  33. Kozii, V., Isobe, H., Venderbos, J. W. F. & Fu, L. Nematic superconductivity stabilized by density wave fluctuations: possible application to twisted bilayer graphene. Phys. Rev. B 99, 144507 (2019).

    Article  ADS  Google Scholar 

  34. Chichinadze, D. V., Classen, L. & Chubukov, A. V. Nematic superconductivity in twisted bilayer graphene. Phys. Rev. B 101, 224513 (2020).

    Article  ADS  Google Scholar 

  35. Kennes, D. M., Lischner, J. & Karrasch, C. Strong correlations and d + id superconductivity in twisted bilayer graphene. Phys. Rev. B 98, 241407 (2018).

    Article  ADS  Google Scholar 

  36. Soejim, T., Parker, D. E., Bultinck, N., Hauschild, J. & Zaletel, M. P. Efficient simulation of moire materials using the density matrix renormalization group. Phys. Rev. B 102, 205111 (2020).

    Article  ADS  Google Scholar 

  37. Kang, J. & Vafek, O. Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer fillingin magic-angle twisted bilayer graphene. Phys. Rev. B 102, 035161 (2020).

    Article  ADS  Google Scholar 

  38. Samajdar, R. et al. Electric-field-tunable electronic nematic order in twisted double-bilayer graphene. 2D Mater. 8, 3 (2021).

    Article  Google Scholar 

  39. Klebl, L., Kennes, D. M. & Honerkamp, C. Functional renormalization group for a large moiré unit cell. Phys. Rev. B 102, 085109 (2020).

    Article  ADS  Google Scholar 

  40. Girit, Ç. Ö. & Zettl, A. Soldering to a single atomic layer. Appl. Phys. Lett. 91, 193512 (2007).

    Article  ADS  Google Scholar 

Download references


S.T. and A.N.P. acknowledge funding from Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0019443. STM equipment support (A.N.P.) and 2D sample synthesis (Y.S.) were provided by the Air Force Office of Scientific Research via grant no. FA9550-16-1-0601. C.R.-V. acknowledges funding from the European Union Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement no. 844271. A.R. acknowledges funding by the European Research Council (ERC-2015-AdG-694097), Grupos Consolidados (IT1249-19) and the Flatiron Institute, a division of the Simons Foundation. L.K., D.M.K. and A.R. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy-Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1-390534769 and Advanced Imaging of Matter (AIM) EXC 2056−390715994 and funding by the Deutsche Forschungsgemeinschaft (DFG) under RTG 1995, within the Priority Program SPP 2244 ‘2DMP’ and GRK 2247. A.R. acknowledges support by the Max Planck Institute-New York City Center for Non-Equilibrium Quantum Phenomena. H.O. is supported by the NSF MRSEC programme grant no. DMR-1420634. Tight-binding and fRG simulations were performed with computing resources granted by RWTH Aachen University under projects rwth0496 and rwth0589. R.S. and M.S.S. acknowledge support from the National Science Foundation under grant no. DMR-2002850. R.M.F. was supported by the DOE-BES under award no. DE-SC0020045. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant no. JPMXP0112101001), JSPS KAKENHI (grant no. JP20H00354) and the CREST (grant no. JPMJCR15F3) JST.

Author information

Authors and Affiliations



C.R.-V. and S.T. performed the STM measurements. Y.S. fabricated the samples for STM measurements. C.R.-V. and S.T. performed experimental data analysis. K.W. and T.T. provided hBN crystals. L.K., L.X. and D.M.K. performed tight-binding calculations. S.T., R.S., M.S.S., J.W.F.V., H.O. and R.M.F. performed continuum-model calculations. R.M.F., A.R. and A.N.P. gave advice. C.R.-V. and S.T. wrote the manuscript with assistance from all authors.

Corresponding author

Correspondence to Abhay N. Pasupathy.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Guy Trambly de Laissardière 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.

Supplementary information

Supplementary Information

Supplementary Figs. 1–8 and Discussion.

Source data

Source Data Fig. 1

Source data for plots in Fig. 1c–e.

Source Data Fig. 2

Source data for plots in Fig. 2c,d.

Source Data Fig. 3

Source data for plots in Fig. 3c,d.

Source Data Fig. 4

Source data for plots in Fig. 4e.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rubio-Verdú, C., Turkel, S., Song, Y. et al. Moiré nematic phase in twisted double bilayer graphene. Nat. Phys. 18, 196–202 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


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