# Cascade of phase transitions and Dirac revivals in magic-angle graphene

## Abstract

Twisted bilayer graphene near the magic angle1,2,3,4 exhibits rich electron-correlation physics, displaying insulating3,4,5,6, magnetic7,8 and superconducting phases4,5,6. The electronic bands of this system were predicted1,2,3,,2 to narrow markedly9,10 near the magic angle, leading to a variety of possible symmetry-breaking ground states11,12,13,14,15,16,17. Here, using measurements of the local electronic compressibility, we show that these correlated phases originate from a high-energy state with an unusual sequence of band population. As carriers are added to the system, the four electronic ‘flavours’, which correspond to the spin and valley degrees of freedom, are not filled equally. Rather, they are populated through a sequence of sharp phase transitions, which appear as strong asymmetric jumps of the electronic compressibility near integer fillings of the moiré lattice. At each transition, a single spin/valley flavour takes all the carriers from its partially filled peers, ‘resetting’ them to the vicinity of the charge neutrality point. As a result, the Dirac-like character observed near charge neutrality reappears after each integer filling. Measurement of the in-plane magnetic field dependence of the chemical potential near filling factor one reveals a large spontaneous magnetization, further substantiating this picture of a cascade of symmetry breaking. The sequence of phase transitions and Dirac revivals is observed at temperatures well above the onset of the superconducting and correlated insulating states. This indicates that the state that we report here, with its strongly broken electronic flavour symmetry and revived Dirac-like electronic character, is important in the physics of magic-angle graphene, forming the parent state out of which the more fragile superconducting and correlated insulating ground states emerge.

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## Data availability

The data that support the plots and other analysis in this work are available from the corresponding author upon request.

## Code availability

The code used in this work is available at https://github.com/erezberg/Dirac_revivals_theory/ .

## Change history

• ### 08 July 2020

The online publication date in the printed version of this article was listed incorrectly as 10 June 2020; the date was correct online.

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## Acknowledgements

We thank U. Aviram, A. H. Macdonald, J. Ruhman, H. Steinberg, S. Todadri, A. Yacoby and E. Zeldov for their suggestions. Work at Weizmann was supported by a Leona M. and Harry B. Helmsley Charitable Trust grant, ISF grants (712539 and 13335/16), a Deloro award, the Sagol Weizmann-MIT Bridge programme, the ERC-Cog (See-1D-Qmatter, no. 647413), ISF Research Grants in the Quantum Technologies and Science Program (994/19 and 2074/19), the DFG (CRC/Transregio 183), the ERC-Cog (HQMAT, no. 817799), EU Horizon 2020 (LEGOTOP 788715) and the Binational Science Foundation (NSF/BMR-BSF grant 2018643). Work at MIT was supported by the National Science Foundation (DMR-1809802), the Center for Integrated Quantum Materials under NSF grant DMR-1231319, and the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4541 to P.J.-H. for device fabrication, transport measurements and data analysis. This work was performed in part at the Harvard University Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Coordinated Infrastructure Network (NNCI), which is supported by the National Science Foundation under NSF ECCS award no. 1541959. D.R.-L. acknowledges partial support from Fundaciòn Bancaria ‘la Caixa’ (LCF/BQ/AN15/10380011) and from the US Army Research Office (grant no. W911NF-17-S-0001). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, A3 Foresight by JSPS and the CREST (JPMJCR15F3), JST.

## Author information

Authors

### Contributions

U.Z., A.R., D.R.-L., P.J.-H. and S.I. designed the experiment. U.Z. and A.R. performed the experiments. D.R.-L. and Y.C. fabricated the twisted bilayer graphene devices. U.Z., A.R. and S.I. analysed the data. R.Q., A.R., F.v.O., Y.O., A.S. and E.B. formulated the theory and performed the Hartree-Fock calculations. K.W. and T.T. supplied the hBN crystals. U.Z., A.R., D.R.-L., A.S., E.B., P.J.-H. and S.I. wrote the manuscript, with input from all authors.

### Corresponding authors

Correspondence to P. Jarillo-Herrero or S. Ilani.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Ivan Brihuega, Fan Zhang and Klaus Ensslin for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

This file contains Supplementary Sections 1-17, including Supplementary Figures 1-18 and Supplementary References.

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Zondiner, U., Rozen, A., Rodan-Legrain, D. et al. Cascade of phase transitions and Dirac revivals in magic-angle graphene. Nature 582, 203–208 (2020). https://doi.org/10.1038/s41586-020-2373-y