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Bulk and edge properties of twisted double bilayer graphene

Nature Physics volume 18, pages 48–53 (2022)Cite this article

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Abstract

The emergence of controlled, two-dimensional moiré materials1,2,3,4,5,6 has uncovered a new platform for investigating topological physics7,8,9. Twisted double bilayer graphene has been predicted to host a topologically non-trivial gapped phase with Chern number equal to two at charge neutrality, when half the flat bands are filled8,9. However, it can be difficult to diagnose topological states using a single measurement because it is ideal to probe the bulk and edge properties at the same time. Here we report a combination of chemical potential measurements, transport measurements and theoretical calculations that show that twisted double bilayer graphene can host metallic edge transport in addition to simultaneously being insulating in the bulk. A Landauer–Büttiker analysis of the measurements on multi-terminal samples allows us to quantitatively assess the edge-state scattering. We interpret these results as signatures of the predicted topological phase at charge neutrality, but further characterization of the edge transport is required to be certain.

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Fig. 1: Sample layout, electrical transport and band structure.
Fig. 2: Chemical potential measurements.
Fig. 3: Gapped bulk and edge states.
Fig. 4: TDBG phase diagrams.

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Data availability

Source data for Figs. 1–4 are provided with this paper. Data that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

A sample Mathematica code for performing the Landauer–Büttiker inversion is implemented for public use at https://doi.org/10.5281/zenodo.5539921. Any software package that can perform a singular-value decomposition is also suitable.

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Acknowledgements

We thank Z.-D. Song and B. Lian for helpful discussions. The work at The University of Texas at Austin was supported by the National Science Foundation (NSF) grants MRSEC DMR-1720595, EECS-1610008 and EECS-2122476; Army Research Office under grant no. W911NF-17-1-0312; and the Welch Foundation grant F-2018-20190330. Work was partly done at the Texas Nanofabrication Facility supported by the NSF grant no. NNCI-2025227. B.A.B. was supported by the DOE grant no. DE-SC0016239, the Schmidt Fund for Innovative Research, Simons Investigator grant no. 404513, the Packard Foundation, the Gordon and Betty Moore Foundation through grant no. GBMF8685 towards the Princeton theory programme, and a Guggenheim Fellowship from the John Simon Guggenheim Memorial Foundation. Further support was provided by the NSF-EAGER no. DMR 1643312, NSFMRSEC no. DMR-1420541 and DMR-2011750, ONR no. N00014-20-1-2303, BSF Israel US foundation no. 2018226, and the Princeton Global Network Funds. J.H.-A. acknowledges support from a Marshall Scholarship funded by the Marshall Aid Commemoration Commission. A.H.M. acknowledges support from the Welch Foundation grant F1473. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant no. JPMXP0112101001), and JSPS KAKENHI (grant nos. JP19H05790 and JP20H00354).

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Authors and Affiliations

  1. Microelectronics Research Center, Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, USA

    Yimeng Wang, G. William Burg & Emanuel Tutuc

  2. Department of Physics, Princeton University, Princeton, NJ, USA

    Jonah Herzog-Arbeitman & B. Andrei Bernevig

  3. Department of Physics, The University of Texas at Austin, Austin, TX, USA

    Jihang Zhu & Allan H. MacDonald

  4. Research Center for Functional Materials, National Institute of Materials Science, Ibaraki, Japan

    Kenji Watanabe

  5. International Center for Materials Nanoarchitectonics, National Institute of Materials Science, Ibaraki, Japan

    Takashi Taniguchi

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  1. Yimeng Wang
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Contributions

Y.W., G.W.B. and E.T. conceived the experiments. Y.W. and G.W.B. fabricated the samples and performed the experiments. J.H.-A., J.Z., A.H.M. and B.A.B. performed the theoretical calculations and analysis. K.W. and T.T. provided the hBN crystals. Y.W., J.H.-A, G.W.B., A.H.M. B.A.B. and E.T. analysed the data. Y.W., J.H.-A. and E.T. wrote the manuscript with input from all authors.

Corresponding author

Correspondence to Emanuel Tutuc.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Sections A–F and Figs. 1–8.

Source data

Source Data Fig. 1

Source data for Fig. 1c,d.

Source Data Fig. 2

Source data for Fig. 2.

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Source Data Fig. 4

Source data for Fig. 4a–c,e,f.

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Wang, Y., Herzog-Arbeitman, J., Burg, G.W. et al. Bulk and edge properties of twisted double bilayer graphene. Nat. Phys. 18, 48–53 (2022). https://doi.org/10.1038/s41567-021-01419-5

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