Electronic correlations in twisted bilayer graphene near the magic angle

Abstract

Twisted bilayer graphene with a twist angle of around 1.1° features a pair of isolated flat electronic bands and forms a platform for investigating strongly correlated electrons. Here, we use scanning tunnelling microscopy to probe the local properties of highly tunable twisted bilayer graphene devices and show that the flat bands deform when aligned with the Fermi level. When the bands are half-filled, we observe the development of gaps originating from correlated insulating states. Near charge neutrality, we find a previously unidentified correlated regime featuring an enhanced splitting of the flat bands. We describe this within a microscopic model that predicts a strong tendency towards nematic ordering. Our results provide insights into symmetry-breaking correlation effects and highlight the importance of electronic interactions for all filling fractions in twisted bilayer graphene.

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Data availability

The experimental data and analyses that support the plots within this paper and the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The computer codes that support the plots within this paper and the findings of this study are available from the corresponding author upon reasonable request

References

1. 1.

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

2. 2.

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

3. 3.

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

4. 4.

Trambly de Laissardière, G., Mayou, D. & Magaud, L. Localization of Dirac electrons in rotated graphene bilayers. Nano Lett. 10, 804–808 (2010).

5. 5.

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

6. 6.

Lopes dos Santos, J. M. B., Peres, N. M. R. & Castro Neto, A. H. Continuum model of the twisted graphene bilayer. Phys. Rev. B 86, 155449 (2012).

7. 7.

Fang, S. & Kaxiras, E. Electronic structure theory of weakly interacting bilayers. Phys. Rev. B 93, 235153 (2016).

8. 8.

Neto, A. C., Guinea, F., Peres, N. M., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).

9. 9.

Luican, A. et al. Single-layer behavior and its breakdown in twisted graphene layers. Phys. Rev. Lett. 106, 126802 (2011).

10. 10.

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

11. 11.

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).

12. 12.

Ohta, T. et al. Evidence for interlayer coupling and moiré periodic potentials in twisted bilayer graphene. Phys. Rev. Lett. 109, 186807 (2012).

13. 13.

Havener, R. W., Liang, Y., Brown, L., Yang, L. & Park, J. Van Hove singularities and excitonic effects in the optical conductivity of twisted bilayer graphene. Nano Lett. 14, 3353–3357 (2014).

14. 14.

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

15. 15.

Kim, K. et al. Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene. Proc. Natl Acad. Sci. USA 114, 3364–3369 (2017).

16. 16.

Huang, S. et al. Topologically protected helical states in minimally twisted bilayer graphene. Phys. Rev. Lett. 121, 037702 (2018).

17. 17.

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

18. 18.

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).

19. 19.

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).

20. 20.

Trambly de Laissardière, G., Mayou, D. & Magaud, L. Numerical studies of confined states in rotated bilayers of graphene. Phys. Rev. B 86, 125413 (2012).

21. 21.

Yan, W. et al. Angle-dependent van Hove singularities in a slightly twisted graphene bilayer. Phys. Rev. Lett. 109, 126801 (2012).

22. 22.

Yin, L.-J., Qiao, J.-B., Zuo, W.-J., Li, W.-T. & He, L. Experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers. Phys. Rev. B 92, 081406 (2015).

23. 23.

Zibrov, A. A. et al. Robust fractional quantum Hall states and continuous quantum phase transitions in a half-filled bilayer graphene Landau level. Nature 549, 360–364 (2017).

24. 24.

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

25. 25.

Zou, L., Po, H. C., Vishwanath, A. & Senthil, T. Band structure of twisted bilayer graphene: emergent symmetries, commensurate approximants, and Wannier obstructions. Phys. Rev. B 98, 085435 (2018).

26. 26.

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).

27. 27.

Kang, J. & Vafek, O. Symmetry, maximally localized Wannier states, and a low-energy model for twisted bilayer graphene narrow bands. Phys. Rev. X 8, 031088 (2018).

28. 28.

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

29. 29.

Xie, M. & MacDonald, A. H. On the nature of the correlated insulator states in twisted bilayer graphene. Preprint at https://arxiv.org/abs/1812.04213 (2018).

30. 30.

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

31. 31.

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).

32. 32.

Kang, J. & Vafek, O. Strong coupling phases of partially filled twisted bilayer graphene narrow bands. Phys. Rev. Lett. 122, 246401 (2019).

33. 33.

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

34. 34.

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

35. 35.

Hejazi, K., Liu, C., Shapourian, H., Chen, X. & Balents, L. Multiple topological transitions in twisted bilayer graphene near the first magic angle. Phys. Rev. B 99, 035111 (2019).

36. 36.

Lilly, M. P., Cooper, K. B., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Anisotropic states of two-dimensional electron systems in high Landau levels: effect of an in-plane magnetic field. Phys. Rev. Lett. 83, 824–827 (1999).

37. 37.

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

38. 38.

Huder, L. et al. Electronic spectrum of twisted graphene layers under heterostrain. Phys. Rev. Lett. 120, 156405 (2018).

39. 39.

Artaud, A. et al. Universal classification of twisted, strained and sheared graphene moiré superlattices. Sci. Rep. 6, 25670 (2016).

40. 40.

Efros, A. L. Coulomb gap in disordered systems. J. Phys. C 9, 2021–2030 (1976).

41. 41.

Ashoori, R. C., Lebens, J. A., Bigelow, N. P. & Silsbee, R. H. Equilibrium tunneling from the two-dimensional electron gas in GaAs: evidence for a magnetic-field-induced energy gap. Phys. Rev. Lett. 64, 681–684 (1990).

42. 42.

Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Coulomb barrier to tunneling between parallel two-dimensional electron systems. Phys. Rev. Lett. 69, 3804–3807 (1992).

43. 43.

Dial, O. E., Ashoori, R. C., Pfeiffer, L. N. & West, K. W. High-resolution spectroscopy of two-dimensional electron systems. Nature 448, 176–179 (2007).

44. 44.

Song, Y.-H. et al. Observation of Coulomb gap in the quantum spin Hall candidate single-layer 1T’-WTe2. Nat. Commun. 9, 4071 (2018).

45. 45.

Moon, B. H. et al. Soft Coulomb gap and asymmetric scaling towards metal–insulator quantum criticality in multilayer MoS2. Nat. Commun. 9, 2052 (2018).

46. 46.

Jung, S. et al. Evolution of microscopic localization in graphene in a magnetic field from scattering resonances to quantum dots. Nat. Phys. 7, 245–251 (2011).

47. 47.

Thomson, A., Chatterjee, S., Sachdev, S. & Scheurer, M. S. Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene. Phys. Rev. B 98, 075109 (2018).

48. 48.

Kerelsky, A. et al. Magic angle spectroscopy. Preprint at https://arxiv.org/abs/1812.08776 (2018).

49. 49.

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

Acknowledgements

We gratefully acknowledge discussions with R. C. Ashoori, P. Jarillo-Herrero, A. Vishwanath, J. Eisenstein, A. Young and H. Beidenkopf. The STM work is in part supported by NSF DMR-1744011. Sample fabrication efforts are supported by the NSF through program NSF CAREER DMR-1753306. S.N.-P. acknowledges support from a KNI-Weathley fellowship. J.A., G.R., F.v.O., S.N.-P. and H.R. acknowledge the support of IQIM (NSF funded physics frontiers center). J.K. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG 406557161), Y.C. a Kwanjeong fellowship, F.v.O. DFG support through CRC 183, and J.A. support from the NSF through grant DMR-1723367. Y.P., A.T. and J.A. are grateful for support from the Walter Burke Institute for Theoretical Physics at Caltech.

Author information

Y.C., J.K. and S.N.-P. conceived the experiment. Y.C. and J.K. performed the measurements. Y.C. made the samples with the help of H.A., R.P. and Y.Z. Y.C., J.K., H.R. and S.N.-P. performed data analysis. Y.P. and A.T. developed the theory guided by F.v.O., J.A. and G.R. Y.C., J.K. and S.N.-P. wrote the manuscript with input from all authors.

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Supplementary information

Supplementary Information

Additional technical and theoretical details, Supplementary Figs. 1–14, Table 1 and refs. 1–16.

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