# Observation of flat bands in twisted bilayer graphene

## Abstract

Transport experiments in twisted bilayer graphene have revealed multiple superconducting domes separated by correlated insulating states1,2,3,4,5. These properties are generally associated with strongly correlated states in a flat mini-band of the hexagonal moiré superlattice as was predicted by band structure calculations6,7,8. Evidence for the existence of a flat band comes from local tunnelling spectroscopy9,10,11,12,13 and electronic compressibility measurements14, which report two or more sharp peaks in the density of states that may be associated with closely spaced Van Hove singularities. However, direct momentum-resolved measurements have proved to be challenging15. Here, we combine different imaging techniques and angle-resolved photoemission with simultaneous real- and momentum-space resolution (nano-ARPES) to directly map the band dispersion in twisted bilayer graphene devices near charge neutrality. Our experiments reveal large areas with a homogeneous twist angle that support a flat band with a spectral weight that is highly localized in momentum space. The flat band is separated from the dispersive Dirac bands, which show multiple moiré hybridization gaps. These data establish the salient features of the twisted bilayer graphene band structure.

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## Data availability

Supporting data are available for this paper in ref. 35. All other data that support the plots within this paper and other 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.

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

4. 4.

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

5. 5.

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

6. 6.

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).

7. 7.

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).

8. 8.

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

9. 9.

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

10. 10.

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

11. 11.

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

12. 12.

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

13. 13.

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

14. 14.

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

15. 15.

Utama, M. I. B. et al. Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist. Nat. Phys. https://doi.org/10.1038/s41567-020-0974-x (2020).

16. 16.

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

17. 17.

Razado-Colambo, I. et al. NanoARPES of twisted bilayer graphene on SiC: absence of velocity renormalization for small angles. Sci. Rep. 6, 27261 (2016).

18. 18.

Marchenko, D. et al. Extremely flat band in bilayer graphene. Sci. Adv. 4, eaau0059 (2018).

19. 19.

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

20. 20.

Hibino, H., Wang, S., Orofeo, C. M. & Kageshima, H. Growth and low-energy electron microscopy characterizations of graphene and hexagonal boron nitride. Prog. Cryst. Growth Charact. Mater. 62, 155–176 (2016).

21. 21.

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

22. 22.

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

23. 23.

Voit, J. et al. Electronic structure of solids with competing periodic potentials. Science 290, 501–503 (2000).

24. 24.

Amorim, B. General theoretical description of angle-resolved photoemission spectroscopy of van der Waals structures. Phys. Rev. B 97, 165414 (2018).

25. 25.

Peng, H. H. et al. Substrate doping effect and unusually large angle Van Hove singularity evolution in twisted bi- and multilayer graphene. Adv. Mater. 29, 1606741 (2017).

26. 26.

Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three dimensional solids. Rev. Mod. Phys. 90, 015001 (2017).

27. 27.

Shen, K. M. et al. Nodal quasiparticles and antinodal charge ordering in Ca2−xNaxCuO2Cl2. Science 307, 901–904 (2005).

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.

Gargiulo, F. & Yazyev, O. V. Structural and electronic transformation in low-angle twisted bilayer graphene. 2D Mater. 5, 015019 (2017).

30. 30.

Lucignano, P., Alfè, D., Cataudella, V., Ninno, D. & Cantele, G. Crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the magic angle ~1.08°. Phys. Rev. B 99, 195419 (2019).

31. 31.

Dudin, P. et al. Angle-resolved photoemission spectroscopy and imaging with a submicrometre probe at the SPECTROMICROSCOPY-3.2L beamline of Elettra. J. Synchrotron Radiat. 17, 445–450 (2010).

32. 32.

de Jong, T. A. et al. Quantitative analysis of spectroscopic low energy electron microscopy data: high-dynamic range imaging, drift correction and cluster analysis. Ultramicroscopy 213, 112913 (2020).

33. 33.

de Jong, T. A. et al. Intrinsic stacking domains in graphene on silicon carbide: a pathway for intercalation. Phys. Rev. Mater. 2, 104005 (2018).

34. 34.

Li, G., Luican, A. & Andrei, E. Y. Self-navigation of a scanning tunneling microscope tip toward a micron-sized graphene sample. Rev. Sci. Instrum. 82, 073701 (2011).

35. 35.

Lisi, S. et al. Source data for ‘Observation of flat bands in twisted bilayer graphene’. Available at https://doi.org/10.26037/yareta:nxtqgcnllzbklcak4qyzi3adv4 (2020).

## Acknowledgements

We thank J. Aarts, S. Nadj-Perge, A. Yazdani, A. Pasupathy, A. Morpurgo, I. Gutierrez-Lezama, H. Henck, F. Groenewoud, K. van Oosten, R.M. Tromp, R. Wijgman and H. Zandvliet for discussions. We thank M. Hesselberth for technical LEEM support. The ARPES work was supported by the Swiss National Science Foundation (SNSF) through grant 200020_184998. L.R. acknowledges support by the SNSF through an Ambizione grant. The STM work was supported by the European Research Council (ERC StG SpinMelt) and by the Dutch Research Council (NWO), as part of the Frontiers of Nanoscience programme, as well as through a Vidi grant (680-47-536). The LEEM work was supported by the NWO as part of the Frontiers of Nanoscience programme. Growth of hBN crystals was supported by the MEXT Element Strategy Initiative to Form Core Research Center (JPMXP0112101001) and the Core Research for Evolutional Science and Technology (JPMJCR15F3), Japan Science and Technology Agency. D.K.E. acknowledges support from the Ministry of Economy and Competitiveness of Spain through the Severo Ochoa programme for Centres of Excellence in R&D (SE5-0522), Funda-ció Privada Cellex, Fundació Privada Mir-Puig, the Generalitat de Catalunya through the CERCA programme, the H2020 Programme (820378), 2D·SIPC and the La Caixa Foundation.

## Author information

Authors

### Contributions

X.L., P.S. and J.R.D. made the TBG devices. T.T. and K.W. contributed hBN materials. S.L., F.M., I.C., E.C. and A.H. performed the nano-ARPES experiments. T.B., V.S. and M.L. performed the STM experiments. T.A.d.J. acquired the LEEM and microscopic low-energy electron diffraction data. L.R. performed the band structure calculations. J.J., S.J.v.d.M. (LEEM), M.A. (STM), D.K.E. (devices) and F.B. (nano-ARPES) were responsible for the project supervision and the provision of resources. V.K., A.G. and A.B. were responsible for the nano-ARPES beamline. S.L., A.T. and F.B. wrote the bulk of the manuscript with contributions from several others. All authors contributed to the scientific discussion of the results.

### Corresponding author

Correspondence to Felix Baumberger.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks Zhongkai Liu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–5 and Supplementary Discussion.

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Lisi, S., Lu, X., Benschop, T. et al. Observation of flat bands in twisted bilayer graphene. Nat. Phys. (2020). https://doi.org/10.1038/s41567-020-01041-x