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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.


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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).

Author information




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.

Corresponding authors

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 Information

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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