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# Strongly correlated Chern insulators in magic-angle twisted bilayer graphene

## 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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## Data availability

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

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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.

## Author information

Authors

### 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.

### Corresponding author

Correspondence to Ali Yazdani.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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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## Supplementary information

### Supplementary Information

This file contains Supplementary Text, Supplementary References and Supplementary Figures 1–14.

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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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• DOI: https://doi.org/10.1038/s41586-020-3028-8

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