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Strongly correlated Chern insulators in magic-angle twisted bilayer graphene

Nature volume 588, pages 610–615 (2020)Cite this article

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Abstract

Interactions between electrons and the topology of their energy bands can create unusual quantum phases of matter. Most topological electronic phases appear in systems with weak electron–electron interactions. The instances in which topological phases emerge only as a result of strong interactions are rare and mostly limited to those realized in intense magnetic fields1. The discovery of flat electronic bands with topological character in magic-angle twisted bilayer graphene (MATBG) has created a unique opportunity to search for strongly correlated topological phases2,3,4,5,6,7,8,9. Here we introduce a local spectroscopic technique using a scanning tunnelling microscope to detect a sequence of topological insulators in MATBG with Chern numbers C = ±1, ±2 and ±3, which form near filling factors of ±3, ±2 and ±1 electrons per moiré unit cell, respectively, and are stabilized by modest magnetic fields. One of the phases detected here (C = +1) was previously observed when the sublattice symmetry of MATBG was intentionally broken by a hexagonal boron nitride substrate, with interactions having a secondary role9. We demonstrate that strong electron–electron interactions alone can produce not only the previously observed phase, but also other unexpected Chern insulating phases in MATBG. The full sequence of phases that we observe can be understood by postulating that strong correlations favour breaking time-reversal symmetry to form Chern insulators that are stabilized by weak magnetic fields. Our findings illustrate that many-body correlations can create topological phases in moiré systems beyond those anticipated from weakly interacting models.

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Fig. 1: Magnetic-field-dependent spectroscopic gaps in MATBG at 200 mK.
Fig. 2: Spectroscopic gap morphology of strongly correlated Chern insulating gaps and ZLLs.
Fig. 3: Quantized magnetic-field response of strongly correlated Chern insulating phases.
Fig. 4: Theoretical interpretation using an interaction-induced, sign-switching Haldane mass.

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Data availability

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

References

  1. Rachel, S. Interacting topological insulators: a review. Rep. Prog. Phys. 81, 116501 (2018).

    Article  ADS  Google Scholar 

  2. Bistritzer, R. & MacDonald, A. H. Moire bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).

    Article  ADS  CAS  Google Scholar 

  3. Suárez Morell, E., Correa, J. D., Vargas, P., Pacheco, M. & Barticevic, Z. Flat bands in slightly twisted bilayer graphene: tight-binding calculations. Phys. Rev. B 82, 121407 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  7. Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  10. Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020); correction 581, E3 (2020).

    Article  ADS  CAS  Google Scholar 

  11. Polshyn, H. et al. Electrical switching of magnetic order in an orbital Chern insulator. Nature 588, 66–70 (2020).

  12. Chen, S. et al. Electrically tunable correlated and topological states in twisted monolayer-bilayer graphene. Nat. Phys. https://doi.org/10.1038/s41567-020-01062-6 (2020).

  13. Liu, J. & Dai, X. Theories for the correlated insulating states and quantum anomalous Hall phenomena in twisted bilayer graphene. Preprint at https://arxiv.org/abs/1911.03760 (2019).

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

    Article  ADS  CAS  Google Scholar 

  15. Haldane, F. D. M. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”. Phys. Rev. Lett. 61, 2015–2018 (1988).

    Article  ADS  CAS  Google Scholar 

  16. Wong, D. et al. A modular ultra-high vacuum millikelvin scanning tunneling microscope. Rev. Sci. Instrum. 91, 023703 (2020).

    Article  ADS  CAS  Google Scholar 

  17. Li, G. et al. Observation of Van Hove singularities in twisted graphene layers. Nat. Phys. 6, 109–113 (2010).

    Article  Google Scholar 

  18. Brihuega, I. et al. Unraveling the intrinsic and robust nature of Van Hove singularities in twisted bilayer graphene by scanning tunneling microscopy and theoretical analysis. Phys. Rev. Lett. 109, 196802 (2012).

    Article  ADS  CAS  Google Scholar 

  19. Wong, D. et al. Local spectroscopy of moiré-induced electronic structure in gate-tunable twisted bilayer graphene. Phys. Rev. B 92, 155409 (2015).

    Article  ADS  Google Scholar 

  20. Xie, Y. et al. Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene. Nature 572, 101–105 (2019).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  23. Choi, Y. et al. Electronic correlations in twisted bilayer graphene near the magic angle. Nat. Phys. 15, 1174–1180 (2019); correction 15, 1205 (2019).

    Article  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  26. Lian, B., Xie, F. & Bernevig, B. A. Landau level of fragile topology. Phys. Rev. B 102, 041402 (2020).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  28. Moon, P., Son, Y. W. & Koshino, M. Optical absorption of twisted bilayer graphene with interlayer potential asymmetry. Phys. Rev. B 90, 155427 (2014).

    Article  ADS  Google Scholar 

  29. Bultinck, N., Chatterjee, S. & Zaletel, M. P. Mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene. Phys. Rev. Lett. 124, 166601 (2020).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  30. Nomura, K. & MacDonald, A. H. Quantum Hall ferromagnetism in graphene. Phys. Rev. Lett. 96, 256602 (2006).

    Article  ADS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  33. Feldman, B. E. et al. Observation of a nematic quantum Hall liquid on the surface of bismuth. Science 354, 316–321 (2016).

    Article  ADS  CAS  Google Scholar 

  34. Randeria, M. T. et al. Interacting multi-channel topological boundary modes in a quantum Hall valley system. Nature 566, 363–367 (2019).

    Article  ADS  Google Scholar 

  35. Středa, P. Theory of quantised Hall conductivity in two dimensions. J. Phys. C 15, L717 (1982).

    Article  ADS  Google Scholar 

  36. Spanton, E. M. et al. Observation of fractional Chern insulators in a van der Waals heterostructure. Science 360, 62–66 (2018).

    Article  ADS  CAS  Google Scholar 

  37. Tomarken, S. L. et al. Electronic compressibility of magic-angle graphene superlattices. Phys. Rev. Lett. 123, 046601 (2019).

    Article  ADS  CAS  Google Scholar 

  38. Abouelkomsan, A., Liu, Z. & Bergholtz, E. J. Particle-hole duality, emergent Fermi liquids, and fractional Chern insulators in moiré flatbands. Phys. Rev. Lett. 124, 106803 (2020).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  39. Ledwith, P. J., Tarnopolsky, G., Khalaf, E. & Vishwanath, A. Fractional Chern insulator states in twisted bilayer graphene: an analytical approach. Phys. Rev. Res. 2, 023237 (2020).

    Article  CAS  Google Scholar 

  40. Repellin, C. & Senthil, T. Chern bands of twisted bilayer graphene: fractional Chern insulators and spin phase transition. Phys. Rev. Res. 2, 023238 (2019).

    Article  Google Scholar 

  41. Deng, Y. et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4. Science 367, 895–900 (2020).

    Article  ADS  CAS  Google Scholar 

  42. Liu, C. et al. Helical Chern insulator phase with broken time-reversal symmetry in MnBi2Te4. Preprint at https://arxiv.org/abs/2001.08401 (2020).

  43. Zhang, Y. H., Mao, D., Cao, Y., Jarillo-Herrero, P. & Senthil, T. Nearly flat Chern bands in moiré superlattices. Phys. Rev. B 99, 075127 (2019).

    Article  ADS  CAS  Google Scholar 

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Acknowledgements

We thank S. Wu, B. Jaeck, X. Liu, K. Hejazi, N. Yuan and L. Fu for discussions. This work was primarily supported by the Gordon and Betty Moore Foundation’s EPiQS initiative grants GBMF4530, GBMF9469 and DOE-BES grant DE-FG02-07ER46419 to A.Y. Other support for the experimental work was provided by NSF-MRSEC through the Princeton Center for Complex Materials NSF-DMR-1420541, NSF-DMR-1904442, ExxonMobil through the Andlinger Center for Energy and the Environment at Princeton, and the Princeton Catalysis Initiative. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan, grant JPMXP0112101001, JSPS KAKENHI grant JP20H00354, and CREST (JPMJCR15F3), JST. B.L. acknowledges support from the Princeton Center for Theoretical Science at Princeton University. B.A.B. acknowledges support from the Department of Energy DE-SC0016239, Simons Investigator Award, the Packard Foundation, the Schmidt Fund for Innovative Research, NSF EAGER grant DMR-1643312, NSF-MRSEC DMR1420541, BSF Israel US foundation number 2018226, ONR number N00014-20-1-2303, and the Princeton Global Network Funds.

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Author notes

  1. These authors contributed equally: Kevin P. Nuckolls, Myungchul Oh, Dillon Wong

Authors and Affiliations

  1. Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA

    Kevin P. Nuckolls, Myungchul Oh, Dillon Wong, B. Andrei Bernevig & Ali Yazdani

  2. Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, USA

    Biao Lian

  3. Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  4. International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

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Contributions

K.P.N., M.O., D.W. and A.Y. designed the experiment. K.P.N., D.W. and M.O. fabricated samples, carried out STM/STS measurements and performed the data analysis. B.L. and B.A.B. performed the theoretical calculations. K.W. and T.T. synthesized the hBN crystals. All authors discussed the results and contributed to the writing of the manuscript.

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Correspondence to Ali Yazdani.

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The authors declare no competing interests.

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Peer review information Nature thanks Vincent Renard, Yayu Wang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Nuckolls, K.P., Oh, M., Wong, D. et al. Strongly correlated Chern insulators in magic-angle twisted bilayer graphene. Nature 588, 610–615 (2020). https://doi.org/10.1038/s41586-020-3028-8

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