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Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene


Flat bands in magic-angle twisted bilayer graphene (MATBG) have recently emerged as a rich platform to explore strong correlations1, superconductivity2,3,4,5 and magnetism3,6,7. However, the phases of MATBG in a magnetic field and what they reveal about the zero-field phase diagram remain relatively uncharted. Here we report a rich sequence of wedge-like regions of quantized Hall conductance with Chern numbers C = ±1, ±2, ±3 and ±4, which nucleate from integer fillings of the moiré unit cell v = ±3, ±2, ±1 and 0, respectively. We interpret these phases as spin- and valley-polarized many-body Chern insulators. The exact sequence and correspondence of the Chern numbers and filling factors suggest that these states are directly driven by electronic interactions, which specifically break the time-reversal symmetry in the system. We further study the yet unexplored higher-energy dispersive bands with a Rashba-like dispersion. The analysis of Landau-level crossings enables a parameter-free comparison to a newly derived ‘magic series’ of level crossings in a magnetic field and provides constraints on the parameters of the Bistritzer–MacDonald MATBG Hamiltonian. Overall, our data provide direct insights into the complex nature of symmetry breaking in MATBG and allow for the quantitative tests of the proposed microscopic scenarios for its electronic phases.

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Fig. 1: Emergent CCIs in MATBG.
Fig. 2: Correlated insulators, superconductors and orbital magnets in MATBG.
Fig. 3: Rashba-like bands and LL crossings in higher-energy dispersive bands.

Data availability

All data that support the plots within this paper and other findings of this study are available from the corresponding authors 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. Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Stepanov, P. et al. Untying the insulating and superconducting orders in magic-angle graphene. Nature 583, 375–378 (2020).

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

    Article  ADS  Google Scholar 

  8. Bistritzer, R. et al. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).

    Article  ADS  Google Scholar 

  9. Wong, D. et al. Cascade of electronic transitions in magic-angle twisted bilayer graphene. Nature 582, 198–202 (2020).

    Article  ADS  Google Scholar 

  10. Zondiner, U. et al. Cascade of phase transitions and Dirac revivals in magic-angle graphene. Nature 582, 203–208 (2020).

    Article  ADS  Google Scholar 

  11. Song, Z. et al. All magic angles in twisted bilayer graphene are topological. Phys. Rev. Lett. 123, 036401 (2019).

    Article  ADS  Google Scholar 

  12. Liu, J. et al. Pseudo Landau level representation of twisted bilayer graphene: band topology and implications on the correlated insulating phase. Phys. Rev. B 99, 155415 (2019).

    Article  ADS  Google Scholar 

  13. Wu, S. et al. Chern insulators and topological flat-bands in magic-angle twisted bilayer graphene. Preprint at (2020).

  14. Nuckolls, K. P. et al. Strongly correlated Chern insulators in magic-angle twisted bilayer graphene. Nature 588, 610–615 (2020).

    Article  ADS  Google Scholar 

  15. Saito, Y. et. al. Hofstadter subband ferromagnetism and symmetry broken Chern insulators in twisted bilayer graphene. Nat. Phys. (2021).

  16. Nomura, K. et al. Quantum Hall ferromagnetism in graphene. Phys. Rev. Lett. 96, 256602 (2006).

    Article  ADS  Google Scholar 

  17. Young, A. F. et al. Spin and valley quantum Hall ferromagnetism in graphene. Nat. Phys. 8, 550–556 (2012).

    Article  Google Scholar 

  18. Song, Y. J. et al. High-resolution tunnelling spectroscopy of a graphene quartet. Nature 467, 185–189 (2010).

    Article  ADS  Google Scholar 

  19. Tschirhart, C. L. et al. Imaging orbital ferromagnetism in a moiré Chern insulator. Preprint at (2020).

  20. Lian, B. et al. TBG IV: exact insulator ground states and phase diagram of twisted bilayer graphene. Preprint at (2020)

  21. Tarnopolsky, G. et al. Origin of magic angles in twisted bilayer graphene. Phys. Rev. Lett. 122, 106405 (2019).

    Article  ADS  Google Scholar 

  22. Stepanov, P. et al. Competing zero-field Chern insulators in superconducting twisted bi-layer graphene. Preprint at (2020)

  23. Taychatanapat, T. et al. Quantum Hall effect and Landau-level crossing of Dirac fermions in trilayer graphene. Nat. Phys. 7, 621–625 (2011).

    Article  Google Scholar 

  24. Datta, B. et al. Strong electronic interaction and multiple quantum Hall ferromagnetic phases in trilayer graphene. Nat. Commun. 8, 14518 (2017).

    Article  ADS  Google Scholar 

  25. Uri, A. et al. Mapping the twist-angle disorder and Landau levels in magic-angle graphene. Nature 581, 47–52 (2020).

    Article  ADS  Google Scholar 

  26. Po, H. et al. Faithful tight-binding models and fragile topology of magic-angle bilayer graphene. Phys. Rev. B 99, 195455 (2019).

    Article  ADS  Google Scholar 

  27. Xu, C. et al. Topological Superconductivity in twisted multilayer graphene. Phys. Rev. Lett. 121, 087001 (2018).

    Article  ADS  Google Scholar 

  28. Liu, X. et al. Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening. Preprint at (2020).

  29. Arora, H. et al. Superconductivity in metallic twisted bilayer graphene stabilized by WSe2. Nature 583, 379–384 (2020).

    Article  ADS  Google Scholar 

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We are grateful for fruitful discussions with A. Yazdani, E. Andrei, D. Abanin and A. Young. Funding: D.K.E. acknowledges support from the Ministry of Economy and Competitiveness of Spain through the ‘Severo Ochoa’ programme for Centres of Excellence in R&D (SE5-0522), Fundació Privada Cellex, Fundació Privada Mir-Puig, the Generalitat de Catalunya through the CERCA programme, funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 852927) and the La Caixa Foundation. B.A.B. was supported by the Department of Energy grant no. DE-SC0016239, the Schmidt Fund for Innovative Research, Simons Investigator grant no. 404513 and the Packard Foundation. Further support was provided by the National Science Foundation EAGER grant no. DMR 1643312, NSF-MRSEC DMR-1420541, US–Israel BSF grant no. 2018226, ONR no. N00014-20-1-2303 and Princeton Global Network Funds. I.D. acknowledges support from the INphINIT ‘la Caixa’ (ID 100010434) fellowship programme (LCF/BQ/DI19/11730030).

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Authors and Affiliations



D.K.E., X.L. and I.D. conceived and designed the experiments. I.D. and X.L. performed the device fabrication and transport measurements. J.H.-A., Z.-D.S. and B.A.B. performed the theoretical modelling of the data. K.W. and T.T. provided the hBN crystals. I.D., X.L., J.H.-A., Z.-D.S., B.A.B. and D.K.E. analysed the data and wrote the paper.

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Correspondence to Xiaobo Lu or Dmitri K. Efetov.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Shubhayu Chatterjee, Feng Wang and Ke Wang for their contribution to the peer review of this work.

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Supplementary Figs. 1–16 and Discussions 1–12.

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Das, I., Lu, X., Herzog-Arbeitman, J. et al. Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene. Nat. Phys. 17, 710–714 (2021).

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