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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Measurement setup and device characterization.
Fig. 2: Asymmetric sawtooth features in inverse compressibility.
Fig. 3: Dependence of the asymmetric sawtooth features at θ = 1.05° on parallel magnetic field and temperature.
Fig. 4: Phase transitions and Dirac revivals model.

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.

References

  1. 1.

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

    ADS  CAS  Article  Google Scholar 

  2. 2.

    Lopes dos Santos, J. M. B., Peres, N. M. R. & Castro Neto, A. H. Graphene bilayer with a twist: electronic structure. Phys. Rev. Lett. 99, 256802 (2007).

    ADS  CAS  Article  Google Scholar 

  3. 3.

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

    ADS  CAS  Article  Google Scholar 

  4. 4.

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

    ADS  CAS  Article  Google Scholar 

  5. 5.

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

    ADS  CAS  Article  Google Scholar 

  6. 6.

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

    ADS  CAS  Article  Google Scholar 

  7. 7.

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

    ADS  CAS  Article  Google Scholar 

  8. 8.

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

    ADS  CAS  Article  Google Scholar 

  9. 9.

    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).

    ADS  Article  Google Scholar 

  10. 10.

    San-Jose, P., González, J. & Guinea, F. Non-Abelian gauge potentials in graphene bilayers. Phys. Rev. Lett. 108, 216802 (2012).

    ADS  CAS  Article  Google Scholar 

  11. 11.

    Po, H. C., Zou, L., Vishwanath, A. & Senthil, T. Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene. Phys. Rev. X 8, 031089 (2018).

    CAS  Google Scholar 

  12. 12.

    Zhang, Y.-H., Po, H. C. & Senthil, T. Landau level degeneracy in twisted bilayer graphene: role of symmetry breaking. Phys. Rev. B 100, 125104 (2019).

    ADS  CAS  Article  Google Scholar 

  13. 13.

    Liu, S., Khalaf, E., Lee, J. Y. & Vishwanath, A. Nematic topological semimetal and insulator in magic angle bilayer graphene at charge neutrality. Preprint at http://arXiv.org/abs/1905.07409 (2019).

  14. 14.

    Po, H. C., Zou, L., Senthil, T. & Vishwanath, A. Faithful tight-binding models and fragile topology of magic-angle bilayer graphene. Phys. Rev. B 99, 195455 (2019).

    ADS  CAS  Article  Google Scholar 

  15. 15.

    Xie, M. & MacDonald, A. H. Nature of the correlated insulator states in twisted bilayer graphene. Phys. Rev. Lett. 124, 097601 (2020).

    ADS  CAS  Article  Google Scholar 

  16. 16.

    Isobe, H., Yuan, N. F. Q. & Fu, L. Unconventional superconductivity and density waves in twisted bilayer graphene. Phys. Rev. X 8, 041041 (2018).

    CAS  Google Scholar 

  17. 17.

    Ochi, M., Koshino, M. & Kuroki, K. Possible correlated insulating states in magic-angle twisted bilayer graphene under strongly competing interactions. Phys. Rev. B 98, 081102 (2018).

    ADS  CAS  Article  Google Scholar 

  18. 18.

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

    Article  Google Scholar 

  19. 19.

    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).

    ADS  CAS  Article  Google Scholar 

  20. 20.

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

    ADS  Article  Google Scholar 

  21. 21.

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

    ADS  CAS  Article  Google Scholar 

  22. 22.

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

    ADS  CAS  Article  Google Scholar 

  23. 23.

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

    CAS  Article  Google Scholar 

  24. 24.

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

    ADS  CAS  Article  Google Scholar 

  25. 25.

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

    ADS  CAS  Article  Google Scholar 

  26. 26.

    Cao, Y. et al. Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene. Phys. Rev. Lett. 117, 116804 (2016).

    ADS  CAS  Article  Google Scholar 

  27. 27.

    Kim, K. et al. van der Waals heterostructures with high accuracy rotational alignment. Nano Lett. 16, 1989–1995 (2016).

    ADS  CAS  Article  Google Scholar 

  28. 28.

    Waissman, J. et al. Realization of pristine and locally tunable one-dimensional electron systems in carbon nanotubes. Nat. Nanotechnol. 8, 569–574 (2013).

    ADS  CAS  Article  Google Scholar 

  29. 29.

    Honig, M. et al. Local electrostatic imaging of striped domain order in LaAlO3/SrTiO3. Nat. Mater. 12, 1112–1118 (2013).

    ADS  CAS  Article  Google Scholar 

  30. 30.

    Yoo, H. et al. Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene. Nat. Mater. 18, 448–453 (2019).

    ADS  CAS  Article  Google Scholar 

  31. 31.

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

    ADS  CAS  Article  Google Scholar 

  32. 32.

    Eisenstein, J., Pfeiffer, L. & West, K. Negative compressibility of interacting two-dimensional electron and quasiparticle gases. Phys. Rev. Lett. 68, 674–677 (1992).

    ADS  CAS  Article  Google Scholar 

  33. 33.

    Cao, Y. et al. Strange metal in magic-angle graphene with near Planckian dissipation. Phys. Rev. Lett. 124, 076801 (2020).

    ADS  CAS  Article  Google Scholar 

  34. 34.

    Polshyn, H. et al. Large linear-in-temperature resistivity in twisted bilayer graphene. Nat. Phys. 15, 1011–1016 (2019).

    CAS  Article  Google Scholar 

Download references

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

Affiliations

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.

Additional information

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

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.