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Dirac spectroscopy of strongly correlated phases in twisted trilayer graphene

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

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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.

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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.

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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.

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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

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  1. Cheng Shen
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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.

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

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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.

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Source Data Extended Data Fig. 1

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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

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