Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Interaction-driven band flattening and correlated phases in twisted bilayer graphene

Nature Physics volume 17, pages 1375–1381 (2021)Cite this article

Subjects

Abstract

Flat electronic bands, characteristic of ‘magic-angle’ twisted bilayer graphene, host many correlated phenomena1,2,3,4,5,6,7,8,9. Nevertheless, many properties of these bands and emerging symmetry-broken phases are still poorly understood. Here we use scanning tunnelling spectroscopy to examine the evolution of the twisted bilayer graphene bands and related gapped phases as the twist angle between the two graphene layers changes. We detect filling-dependent flattening of the bands that is appreciable even when the angle is well above the magic angle value and so the material is nominally in a weakly correlated regime. Upon approaching the magic angle, we further show that the most prominent correlated gaps begin to emerge when band flattening is maximized around certain integer fillings of electrons per moiré unit cell. Our observations are consistent with a model that suggests that a significant enhancement of the density of states caused by the band flattening triggers a cascade of symmetry-breaking transitions. Finally, we explore the temperature dependence of the cascade and identify gapped features that develop in a broad range of band fillings where superconductivity is expected. Our results highlight the role of interaction-driven band flattening in defining the electronic properties of twisted bilayer graphene.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Filling-dependent band structure deformation of TBG at twist angle θ = 1.32°.
Fig. 2: Evolution of LLs with twist angle and correlated gaps at B = 8 T.
Fig. 3: Emergence of zero-field correlated gaps and symmetry-breaking cascade.
Fig. 4: Temperature dependence of correlated gaps around ν = ±2 and the symmetry-breaking cascade.

Similar content being viewed by others

Data availability

The data reported in Figs. 1–4 can be found on zenodo: https://zenodo.org/record/5173159. Other data that support the findings of this study are available from the corresponding authors on reasonable request.

Code availability

The code that supports the findings of this study is available from the corresponding authors on reasonable request.

References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Nuckolls, K. P. et al. Strongly correlated Chern insulators in magic-angle twisted bilayer graphene. Nature 588, 610–615 (2020).

    Article  ADS  Google Scholar 

  8. Choi, Y. et al. Correlation-driven topological phases in magic-angle twisted bilayer graphene. Nature 589, 536–541 (2021).

    Article  ADS  Google Scholar 

  9. Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Flavour Hund’s coupling, Chern gaps and charge diffusivity in moiré graphene. Nature 592, 43–48 (2021).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. 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).

    Article  ADS  Google Scholar 

  12. Uchida, K., Furuya, S., Iwata, J.-I. & Oshiyama, A. Atomic corrugation and electron localization due to moiré patterns in twisted bilayer graphenes. Phys. Rev. B 90, 155451 (2014).

    Article  ADS  Google Scholar 

  13. Jung, J., Raoux, A., Qiao, Z. & MacDonald, A. H. Ab initio theory of moiré superlattice bands in layered two-dimensional materials. Phys. Rev. B 89, 205414 (2014).

    Article  ADS  Google Scholar 

  14. Nam, N. N. T. & Koshino, M. Lattice relaxation and energy band modulation in twisted bilayer graphene. Phys. Rev. B 96, 075311 (2017).

    Article  ADS  Google Scholar 

  15. Carr, S., Fang, S., Zhu, Z. & Kaxiras, E. Exact continuum model for low-energy electronic states of twisted bilayer graphene. Phys. Rev. Res. 1, 013001 (2019).

    Article  Google Scholar 

  16. Guinea, F. & Walet, N. R. Continuum models for twisted bilayer graphene: effect of lattice deformation and hopping parameters. Phys. Rev. B 99, 205134 (2019).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. Parker, D. E., Soejima, T., Hauschild, J., Zaletel, M. P. & Bultinck, N. Strain-induced quantum phase transitions in magic-angle graphene. Phys. Rev. Lett. 127, 027601 (2021).

    Article  ADS  Google Scholar 

  19. Guinea, F. & Walet, N. R. Electrostatic effects, band distortions, and superconductivity in twisted graphene bilayers. Proc. Natl Acad. Sci. USA 115, 13174–13179 (2018).

    Article  ADS  Google Scholar 

  20. Goodwin, Z. A. H., Vitale, V., Liang, X., Mostofi, A. A. & Lischner, J. Hartree theory calculations of quasiparticle properties in twisted bilayer graphene. Electron. Struct. 2, 034001 (2020).

    Article  ADS  Google Scholar 

  21. Cea, T., Walet, N. R. & Guinea, F. Electronic band structure and pinning of Fermi energy to Van Hove singularities in twisted bilayer graphene: a self-consistent approach. Phys. Rev. B 100, 205113 (2019).

    Article  ADS  Google Scholar 

  22. Cea, T. & Guinea, F. Band structure and insulating states driven by Coulomb interaction in twisted bilayer graphene. Phys. Rev. B 102, 045107 (2020).

    Article  ADS  Google Scholar 

  23. Rademaker, L., Abanin, D. A. & Mellado, P. Charge smoothening and band flattening due to Hartree corrections in twisted bilayer graphene. Phys. Rev. B 100, 205114 (2019).

    Article  ADS  Google Scholar 

  24. Klebl, L., Goodwin, Z. A. H., Mostofi, A. A., Kennes, D. M. & Lischner, J. Importance of long-ranged electron–electron interactions for the magnetic phase diagram of twisted bilayer graphene. Phys. Rev. B 103, 195127 (2021).

    Article  ADS  Google Scholar 

  25. Rademaker, L. & Mellado, P. Charge-transfer insulation in twisted bilayer graphene. Phys. Rev. B 98, 235158 (2018).

    Article  ADS  Google Scholar 

  26. Carr, S., Fang, S., Po, H. C., Vishwanath, A. & Kaxiras, E. Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: first-principles approach. Phys. Rev. Res. 1, 033072 (2019).

    Article  Google Scholar 

  27. Calderón, M. J. & Bascones, E. Interactions in the 8-orbital model for twisted bilayer graphene. Phys. Rev. B 102, 155149 (2020).

    Article  ADS  Google Scholar 

  28. Saito, Y. et al. Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene. Nat. Phys. 17, 478–481 (2021).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Arora, H. S. et al. Superconductivity in metallic twisted bilayer graphene stabilized by WSe2. Nature 583, 379–384 (2020).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. Koshino, M. et al. Maximally localized wannier orbitals and the extended Hubbard model for twisted bilayer graphene. Phys. Rev. X 8, 031087 (2018).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  36. Xie, M. & MacDonald, A. H. Weak-field Hall resistivity and spin/valley flavor symmetry breaking in MAtBG. Preprint at https://arxiv.org/abs/2010.07928 (2020).

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

    Article  ADS  Google Scholar 

  38. Hofmann, J. S., Berg, E. & Chowdhury, D. Superconductivity, pseudogap, and phase separation in topological flat bands. Phys. Rev. B 102, 201112 (2020).

    Article  ADS  Google Scholar 

  39. Bernevig, B. A. et al. Twisted bilayer graphene. V. Exact analytic many-body excitations in Coulomb Hamiltonians: charge gap, Goldstone modes, and absence of Cooper pairing. Phys. Rev. B 103, 205415 (2021).

    Article  ADS  Google Scholar 

  40. Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene. Nature 590, 249–255 (2021).

    Article  ADS  Google Scholar 

  41. Hao, Z. et al. Electric field tunable unconventional superconductivity in alternating twist magic-angle trilayer graphene. Science 371, 1133–1138 (2021).

    Article  ADS  Google Scholar 

  42. Saito, Y. et al. Isospin Pomeranchuk effect in twisted bilayer graphene. Nature 592, 220–224 (2021).

    Article  ADS  Google Scholar 

  43. Rozen, A. et al. Entropic evidence for a Pomeranchuk effect in magic-angle graphene. Nature 592, 214–219 (2021).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge discussions with F. Guinea, F. von Oppen, and G. Refael. Funding: This work has been primarily supported by NSF grants DMR-2005129 and DMR-172336; and Army Research Office under Grant Award W911NF17-1-0323. Part of the STM characterization has been supported by NSF CAREER programme (DMR-1753306). Nanofabrication efforts have been in part supported by DOE-QIS programme (DE-SC0019166). S.N.-P. acknowledges support from the Sloan Foundation. J.A. and S.N.-P. also acknowledge support of the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant GBMF1250; C.L. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative (grant GBMF8682). A.T. and J.A. are grateful for the support of the Walter Burke Institute for Theoretical Physics at Caltech. Y.P. acknowledges support from the startup fund from California State University, Northridge. Y.C. and H.K. acknowledge support from the Kwanjeong Fellowship.

Author information

Author notes

  1. These authors contributed equally to this work: Youngjoon Choi, Hyunjin Kim.

Authors and Affiliations

  1. T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA, USA

    Youngjoon Choi, Hyunjin Kim, Robert Polski, Yiran Zhang & Stevan Nadj-Perge

  2. Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA

    Youngjoon Choi, Hyunjin Kim, Cyprian Lewandowski, Alex Thomson, Robert Polski, Yiran Zhang, Jason Alicea & Stevan Nadj-Perge

  3. Department of Physics, California Institute of Technology, Pasadena, CA, USA

    Youngjoon Choi, Hyunjin Kim, Cyprian Lewandowski, Alex Thomson, Yiran Zhang & Jason Alicea

  4. Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, USA

    Cyprian Lewandowski, Alex Thomson & Jason Alicea

  5. Department of Physics and Astronomy, California State University, Northridge, CA, USA

    Yang Peng

  6. National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe & Takashi Taniguchi

Authors
  1. Youngjoon Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hyunjin Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cyprian Lewandowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yang Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Alex Thomson
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Robert Polski
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yiran Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Kenji Watanabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Takashi Taniguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Jason Alicea
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Stevan Nadj-Perge
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Y.C. and H.K. fabricated samples with the help of R.P. and Y.Z., and performed STM measurements. Y.C., H.K. and S.N.-P. analysed the data. C.L. and Y.P. implemented TBG models. C.L., Y.P. and A.T. provided theoretical analysis of the model results supervised by J.A. S.N.-P. supervised the project. Y.C., H.K., C.L., Y.P., A.T., J.A. and S.N.-P. wrote the manuscript with input from other authors.

Corresponding author

Correspondence to Stevan Nadj-Perge.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks the anonymous reviewers 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

Supplementary Discussion and Figs. 1–16.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Choi, Y., Kim, H., Lewandowski, C. et al. Interaction-driven band flattening and correlated phases in twisted bilayer graphene. Nat. Phys. 17, 1375–1381 (2021). https://doi.org/10.1038/s41567-021-01359-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-021-01359-0

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing