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.

Dirac spectroscopy of strongly correlated phases in twisted trilayer graphene

Nature Materials volume 22, pages 316–321 (2023)Cite this article

Subjects

Abstract

Magic-angle twisted trilayer graphene (MATTG) hosts flat electronic bands, and exhibits correlated quantum phases with electrical tunability. In this work, we demonstrate a spectroscopy technique that allows for dissociation of intertwined bands and quantification of the energy gaps and Chern numbers C of the correlated states in MATTG by driving band crossings between Dirac cone Landau levels and energy gaps in the flat bands. We uncover hard correlated gaps with C = 0 at integer moiré unit cell fillings of ν = 2 and 3 and reveal charge density wave states originating from van Hove singularities at fractional fillings ν = 5/3 and 11/3. In addition, we demonstrate displacement-field-driven first-order phase transitions at charge neutrality and ν = 2, which are consistent with a theoretical strong-coupling analysis, implying C2T symmetry breaking. Overall, these properties establish a diverse electrically tunable phase diagram of MATTG and provide an avenue for investigating other related systems hosting both steep and flat bands.

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

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

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

Fig. 1: Band crossings and zero Chern numbers in the flat band of MATTG.
Fig. 2: Charge density wave at fractional fillings ν = 5/3 and 11/3.
Fig. 3: Extraction of the interaction-driven gap at v = 2.
Fig. 4: Displacement-field-induced phase transitions.

Data availability

Source data for the main figures and the Extended Data figures are provided along with this paper. Other supporting data are available from the corresponding author upon reasonable request. Source data are provided with this paper.

References

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

    Article  CAS  Google Scholar 

  2. Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).

    Article  CAS  Google Scholar 

  3. Shen, C. et al. Correlated states in twisted double bilayer graphene. Nat. Phys. 16, 520–525 (2020).

    Article  CAS  Google Scholar 

  4. Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).

    Article  CAS  Google Scholar 

  5. Cao, Y. et al. Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene. Nature 583, 215–220 (2020).

    Article  CAS  Google Scholar 

  6. Liu, X. et al. Tunable spin-polarized correlated states in twisted double bilayer graphene. Nature 583, 221–225 (2020).

    Article  CAS  Google Scholar 

  7. Chen, S. et al. Electrically tunable correlated and topological states in twisted monolayer–bilayer graphene. Nat. Phys. 17, 374–380 (2021).

    Article  CAS  Google Scholar 

  8. Chen, G. et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys. 15, 237–241 (2019).

    Article  CAS  Google Scholar 

  9. Polshyn, H. et al. Electrical switching of magnetic order in an orbital Chern insulator. Nature 588, 66–70 (2020).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  13. Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science (1979) 365, 605–608 (2019).

    CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  15. Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  17. Das, I. et al. Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene. Nat. Phys. 17, 710–714 (2021).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  19. Wu, S., Zhang, Z., Watanabe, K., Taniguchi, T. & Andrei, E. Y. Chern insulators, van Hove singularities and topological flat bands in magic-angle twisted bilayer graphene. Nat. Mater. 20, 488–494 (2021).

    Article  CAS  Google Scholar 

  20. 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  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  22. 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  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  24. Cao, Y., Park, J. M., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Pauli-limit violation and re-entrant superconductivity in moiré graphene. Nature 595, 526–531 (2021).

    Article  CAS  Google Scholar 

  25. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    Article  CAS  Google Scholar 

  26. Zhang, Y., Tan, Y.-W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

    Article  CAS  Google Scholar 

  27. Pierce, A. T. et al. Unconventional sequence of correlated Chern insulators in magic-angle twisted bilayer graphene. Nat. Phys. 17, 1210–1215 (2021).

    Article  CAS  Google Scholar 

  28. Kwan, Y. H. et al. Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene. Phys. Rev. X 11, 41063 (2021).

    CAS  Google Scholar 

  29. Kim, H. et al. Evidence for unconventional superconductivity in twisted trilayer graphene. Nature 606, 494–500 (2022).

    Article  CAS  Google Scholar 

  30. Khalaf, E., Kruchkov, A. J., Tarnopolsky, G. & Vishwanath, A. Magic angle hierarchy in twisted graphene multilayers. Phys. Rev. B 100, 85109 (2019).

    Article  CAS  Google Scholar 

  31. Carr, S. et al. Ultraheavy and ultrarelativistic Dirac quasiparticles in sandwiched graphenes. Nano Lett. 20, 3030–3038 (2020).

    Article  CAS  Google Scholar 

  32. Lei, C., Linhart, L., Qin, W., Libisch, F. & MacDonald, A. H. Mirror symmetry breaking and lateral stacking shifts in twisted trilayer graphene. Phys. Rev. B 104, 35139 (2021).

    Article  CAS  Google Scholar 

  33. Li, X., Wu, F. & MacDonald, A. H. Electronic structure of single-twist trilayer graphene. Preprint at https://arxiv.org/abs/1907.12338 (2019).

  34. Khalaf, E., Chatterjee, S., Bultinck, N., Zaletel, M. P. & Vishwanath, A. Charged skyrmions and topological origin of superconductivity in magic-angle graphene. Sci. Adv. 7, 5299 (2021).

    Article  Google Scholar 

  35. Xie, F., Regnault, N., Călugăru, D., Bernevig, B. A. & Lian, B. Twisted symmetric trilayer graphene. II. Projected Hartree–Fock study. Phys. Rev. B 104, 115167 (2021).

    Article  CAS  Google Scholar 

  36. Christos, M., Sachdev, S. & Scheurer, M. S. Correlated insulators, semimetals, and superconductivity in twisted trilayer graphene. Phys. Rev. X 12, 021018 (2022).

    CAS  Google Scholar 

  37. Ledwith, P. J. et al. TB or not TB? Contrasting properties of twisted bilayer graphene and the alternating twist n-layer structures (n = 3, 4, 5,…). Preprint at https://arxiv.org/abs/2111.11060 (2021).

  38. Lin, J.-X. et al. Spin-orbit–driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene. Science 375, eabh2889 (2022).

  39. Huang, C., Wei, N., Qin, W. & MacDonald, A. Pseudospin paramagnons and the superconducting dome in magic angle twisted bilayer graphene. Preprint at https://arxiv.org/abs/2110.13351 (2021).

  40. Park, J. M. et al. Robust superconductivity in magic-angle multilayer graphene family. Nat. Mater. 21, 877–883 (2022).

    Article  CAS  Google Scholar 

  41. Zhang, Y. et al. Promotion of superconductivity in magic-angle graphene multilayers. Science (1979) 377, 1538–1543 (2022).

    CAS  Google Scholar 

Download references

Acknowledgements

We thank B. Andrei Bernevig, L. Xian and Q. Wu for fruitful discussions and I. Das, A. Jaoui, C.-W. Cho and B.A. Piot for the help with cryogenic measurements. P.J.L. acknowledges fruitful discussions with M. Christos and support by the Department of Defense (DoD) through the National Defense Science and Engineering Graduate Fellowship (NDSEG) Program. E.K. was supported by the German National Academy of Sciences Leopoldina through grant number LPDS 2018-02. A.V. was supported by a Simons Investigator award and by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (grant number 651440). 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), Fundació Privada Cellex, Fundació Privada Mir-Puig, the Generalitat de Catalunya through the CERCA programme, funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 852927). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant number JPMXP0112101001) and JSPS KAKENHI (grant numbers 19H05790, 20H00354 and 21H05233).

Author information

Authors and Affiliations

  1. ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona, Spain

    Cheng Shen & Dmitri K. Efetov

  2. Department of Physics, Harvard University, Cambridge, MA, USA

    Patrick J. Ledwith, Eslam Khalaf & Ashvin Vishwanath

  3. National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe & Takashi Taniguchi

  4. Fakultät für Physik, Ludwig-Maximilians-Universität, Schellingstrasse 4, 80799 München, Germany

    Dmitri K. Efetov

  5. Munich Center for Quantum Science and Technology (MCQST), München, Germany

    Dmitri K. Efetov

Authors
  1. Cheng Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrick J. Ledwith
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kenji Watanabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Takashi Taniguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Eslam Khalaf
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ashvin Vishwanath
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Dmitri K. Efetov
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

C.S. and D.K.E. conceived of the project. C.S. fabricated devices, performed transport measurements and analysed the experimental data. P.J.L, E.K. and A.V. performed the numeric simulations. K.W. and T.T. provided the hBN crystals. C.S., P.J.L., E.K., A.V. and D.K.E. discussed the data. C.S., P.J.L., E.K., A.V. and D.K.E. wrote the paper.

Corresponding authors

Correspondence to Cheng Shen or Dmitri K. Efetov.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Materials thanks Oleg Yazyev and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

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

Extended data

Extended Data Fig. 1 Landau fan diagram and Landau level crossing at D=0V/nm.

a, b, Landau fan diagram shown by longitudinal resistance Rxx and transverse Hall resistance Rxy. c, schematic of Landau level structure as observed in panel (a) and panel (b).

Source data

Extended Data Fig. 2 Phase diagram in perpendicular magnetic field and chemical potential measurement at D=0V/nm.

a, four types of phases in perpendicular magnetic field when Dirac cone coexists with moiré flat band. The dash lines denote phase boundaries. Phases II and III correspond to partially filling Nth D-LL, which shows finite band broadening due to disorder effects. The phase boundary between phase II and III, namely AN and BN is marked with solid line. In illustration schematics for each phase, the emergent correlated gap is shown by flat band splitting. b, chemical potential measurement at D = 0V/nm. The dark cyan dots show energy difference between flat band and Dirac cone vertex, which is obtained via phase III with D-LL index N = 1. The yellow dash line denotes a tentative plotting of Dirac cone shifting as a function of charge filling, where the zero energy corresponds to energy of flat band charge neutrality.

Source data

Extended Data Fig. 3 Zoom-in Landau fan diagram around v=2 at moderate displacement field.

The top, middle and bottom panels are mapping plots of longitudinal resistance Rxx of two neighbour regions R1 and R2 and Hall resistance Rxy, respectively. From the left to the right panel, displacement field D is D = 0,0.05,0.1,0.15 and 0.2V/nm in sequence.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–11 and Discussion.

Source data

Source Data Fig. 1

Statistical source data

Source Data Fig. 2

Statistical source data

Source Data Fig. 3

Statistical source data

Source Data Fig. 4

Statistical source data

Source Data Extended Data Fig. 1

Statistical source data

Source Data Extended Data Fig. 2

Statistical source data

Source Data Extended Data Fig. 3

Statistical source data

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shen, C., Ledwith, P.J., Watanabe, K. et al. Dirac spectroscopy of strongly correlated phases in twisted trilayer graphene. Nat. Mater. 22, 316–321 (2023). https://doi.org/10.1038/s41563-022-01428-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-022-01428-6

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