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.

Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist

Abstract

Bilayer graphene has been predicted to host a moiré miniband with flat dispersion if the layers are stacked at specific twist angles known as the ’magic angles’1,2. Recently, twisted bilayer graphene (tBLG) with a magic angle twist was reported to exhibit a correlated insulating state and superconductivity3,4, where the presence of the flat miniband in the system is thought to be essential for the emergence of these ordered phases in the transport measurements. Although tunnelling spectroscopy5,6,7,8,9 and electronic compressibility measurements10 in tBLG have found a van Hove singularity that is consistent with the presence of the flat miniband, a direct observation of the flat dispersion in the momentum space of such a moiré miniband in tBLG is still lacking. Here, we report the visualization of this flat moiré miniband by using angle-resolved photoemission spectroscopy with nanoscale resolution. The high spatial resolution of this technique enabled the measurement of the local electronic structure of the tBLG. The measurements demonstrate the existence of the flat moiré band near the charge neutrality for tBLG close to the magic angle at room temperature.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: tBLG near magic angle twist on hBN substrate.
Fig. 2: Moiré pattern visualized with MIM from tBLG in the location with flat electronic band feature.
Fig. 3: Electronic structure of tBLG and the visualization of the flat band dispersion.

Data availability

The data that support the plots within this paper and other finding of this study are available from the corresponding author upon reasonable request. Simulation parameters are provided in the Supplementary Information and can be used as in LAMMPS or with the KIM MD potential database.

References

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

    ADS  Article  Google Scholar 

  2. 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 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  11. McChesney, J. L. et al. Extended van hove singularity and superconducting instability in doped graphene. Phys. Rev. Lett. 104, 136803 (2010).

    ADS  Article  Google Scholar 

  12. Pierucci, D. et al. Evidence for flat bands near the fermi level in epitaxial rhombohedral multilayer graphene. ACS Nano 9, 5432–5439 (2015).

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  14. Senkovskiy, B. V. et al. Boron-doped graphene nanoribbons: electronic structure and raman fingerprint. ACS Nano 12, 7571–7582 (2018).

    Article  Google Scholar 

  15. Henck, H. et al. Flat electronic bands in long sequences of rhombohedral-stacked graphene. Phys. Rev. B 97, 245421 (2018).

    ADS  Article  Google Scholar 

  16. Ehlen, N. et al. Origin of the flat in heavily Cs-doped graphene. ACS Nano 14, 1055–1059 (2019).

    Article  Google Scholar 

  17. Bao, C. et al. Stacking-dependent electronic structure of trilayer graphene resolved by nanospot angle-resolved photoemission spectroscopy. Nano Lett. 17, 1564–1568 (2017).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  20. Kim, K. S. et al. Coexisting massive and massless dirac fermions in symmetry-broken bilayer graphene. Nat. Mater. 12, 887–892 (2013).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  23. Bultinck, N., Chatterjee, S. & Zaletel, M. P. Mechanism for anomalous hall ferromagnetism in twisted bilayer graphene. Phys. Rev. Lett. 124, 166601 (2020).

    ADS  MathSciNet  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  25. Wang, E. et al. Gaps induced by inversion symmetry breaking and second-generation dirac cones in graphene/hexagonal boron nitride. Nat. Phys. 12, 1111–1115 (2016).

    Article  Google Scholar 

  26. Razado-Colambo, I. et al. Nanoarpes of twisted bilayer graphene on sic: Absence of velocity renormalization for small angles. Sci. Rep. 6, 27261 (2016).

    ADS  Article  Google Scholar 

  27. Peng, 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).

    Article  Google Scholar 

  28. Lai, K. et al. Nanoscale electronic inhomogeneity in In2Se3 nanoribbons revealed by microwave impedance microscopy. Nano Lett. 9, 1265–1269 (2009).

    ADS  Article  Google Scholar 

  29. Mallet, P., Brihuega, I., Cherkez, V., Gómez-Rodríguez, J. M. & Veuillen, J.-Y. Friedel oscillations in graphene-based systems probed by scanning tunneling microscopy. C. R. Phys. 17, 294–301 (2016).

    ADS  Article  Google Scholar 

  30. Joucken, F. et al. Visualizing the effect of an electrostatic gate with angle-resolved photoemission spectroscopy. Nano Lett. 19, 2682–2687 (2019).

    ADS  Article  Google Scholar 

  31. Nguyen, P. V. et al. Visualizing electrostatic gating effects in two-dimensional heterostructures. Nature 572, 220–223 (2019).

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  34. Lai, K., Kundhikanjana, W., Kelly, M. A. & Shen, Z.-X. Nanoscale microwave microscopy using shielded cantilever probes. Appl. Nanosci. 1, 13–18 (2011).

    ADS  Article  Google Scholar 

  35. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comp. Phys. 117, 1–19 (1995).

    ADS  Article  Google Scholar 

  36. Leconte, N., An, J. J., Javvaji, J. & Jung, J. Relaxation effects in twisted bilayer graphene: a multiscale approach. Preprint at https://arxiv.org/abs/1910.12805 (2019).

  37. Wen, M., Carr, S., Fang, S., Kaxiras, E. & Tadmor, E. B. Dihedral-angle-corrected registry-dependent interlayer potential for multilayer graphene structures. Phys. Rev. B 98, 235404 (2018).

    ADS  Article  Google Scholar 

  38. Leconte, N., Jung, J., Lebègue, S. & Gould, T. Moire-pattern interlayer potentials in van der waals materials in the random-phase approximation. Phys. Rev. B 96, 195431 (2017).

    ADS  Article  Google Scholar 

  39. Jung, J. & MacDonald, A. H. Accurate tight-binding models for the π bands of bilayer graphene. Phys. Rev. B 89, 035405 (2014).

    ADS  Article  Google Scholar 

  40. Ku, W., Berlijn, T. & Lee, C.-C. Unfolding first-principles band structures. Phys. Rev. Lett. 104, 216401 (2010).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank S. Kahn for technical assistance in the sample fabrication setup. This work was supported as part of the Center for Novel Pathways to Quantum Coherence in Materials, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no. DE-AC02-05CH11231. The MIM measurements were supported by the Materials Sciences and Engineering Division of the US Department of Energy under contract no. DE-AC02-05-CH11231 (sp2-Bonded Materials Program KC2207). The MIM instrument at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no. DE-AC02-05CH11231. Support for K.W. and T.T. from the Elemental Strategy Initiative, conducted by the MEXT, Japan and CREST (JPMJCR15F3) is acknowledged. J.S.T. and N.L. acknowledge the Korean National Research Foundation grant no. NRF-2018R1C1B6004437 and the Korea Research Fellowship Program funded by the Ministry of Science and ICT (KRF-2016H1D3A1023826), as well as the computational resources by KISTI through grant no. KSC-2018-CHA-0077. J.J. was supported by the Samsung Science and Technology Foundation under project SSTF-BAA1802-06.

Author information

Authors and Affiliations

Authors

Contributions

F.W., E.R. and M.I.B.U. conceived the project. M.I.B.U. developed the sample preparation method and carried out sample fabrication with the assistance of J.Z. The nanoARPES experiments were performed by R.J.K., A.B. and E.R. The nanoARPES setup was developed and maintained by R.J.K., C.J., A.B. and E.R. The nanoARPES experimental data were analysed by M.I.B.U. and F.W. with A.B. and E.R. providing guidance. K.L. contributed to the MIM instrumentation setup. K.L. and M.I.B.U. performed AFM and MIM and analysed the data with P.D.A., A.W.B. and A.Z. providing guidance. J.J. and N.L. calculated the spectral functions. H.L. and S.Z. contributed to the surface cleaning process. L.J. performed scanning near field optical microscopy. K.W. and T.T. grew the hBN single crystal. F.W. and E.R. supervised the project. M.I.B.U. and F.W. wrote the manuscript with input from all authors.

Corresponding authors

Correspondence to Jeil Jung, Aaron Bostwick or Feng Wang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Figs. 1–9 with the accompanying discussion.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Utama, M.I.B., Koch, R.J., Lee, K. et al. Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist. Nat. Phys. 17, 184–188 (2021). https://doi.org/10.1038/s41567-020-0974-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-020-0974-x

Further reading

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