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Local atomic stacking and symmetry in twisted graphene trilayers

Nature Materials volume 23, pages 323–330 (2024)Cite this article

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Abstract

Moiré superlattices formed by twisting trilayers of graphene are a useful model for studying correlated electron behaviour and offer several advantages over their formative bilayer analogues, including a more diverse collection of correlated phases and more robust superconductivity. Spontaneous structural relaxation alters the behaviour of moiré superlattices considerably and has been suggested to play an important role in the relative stability of superconductivity in trilayers. Here we use an interferometric four-dimensional scanning transmission electron microscopy approach to directly probe the local graphene layer alignment over a wide range of trilayer graphene structures. Our results inform a thorough understanding of how reconstruction modulates the local lattice symmetries crucial for establishing correlated phases in twisted graphene trilayers, evincing a relaxed structure that is markedly different from that proposed previously.

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Fig. 1: Interferometric 4D-STEM dark-field imaging of selected interfaces.
Fig. 2: Reconstruction in AtA and tAB trilayers.
Fig. 3: Atomic stacking in slightly misaligned TTLG.
Fig. 4: Reconstruction patterns and trends in TTLG.
Fig. 5: Heterostrain effects.

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Data availability

The data supporting the findings of this study are available within the Article and its Supplementary Information files. Datasets can be found at https://doi.org/10.5281/zenodo.4459669.

Code availability

The code developed for data analysis in this study can be accessed within the TrilayerTEM subdirectory at https://github.com/bediakolab/bediakolab_scripts.

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Acknowledgements

We thank P. Kim, J. Ciston, K. Bustillo and C. Ophus for in-person and epistolary discussions. This material is based upon work supported by the US National Science Foundation Early Career Development Program (CAREER) under award no. 2238196 (D.K.B.). I.M.C. acknowledges a predoctoral fellowship award under contract FA9550-21-F-0003 through the National Defense Science and Engineering Graduate (NDSEG) Fellowship Program, sponsored by the Air Force Research Laboratory, the Office of Naval Research and the Army Research Office. C.G. was supported by a grant from the W.M. Keck Foundation (award no. 993922). Experimental work at the Molecular Foundry, Lawrence Berkeley National Laboratory was supported by the Office of Science, Office of Basic Energy Sciences, the US Department of Energy under contract no. DE-AC02-05CH11231. Confocal Raman spectroscopy was supported by a Defense University Research Instrumentation Program grant through the Office of Naval Research under award no. N00014-20-1-2599 (D.K.B.). Other instrumentation used in this work was supported by grants from the Canadian Institute for Advanced Research (CIFAR-Azrieli Global Scholar, award no. GS21-011, D.K.B.), the Gordon and Betty Moore Foundation EPiQS Initiative (award no. 10637, D.K.B.) and the 3M Foundation through the 3M Non-Tenured Faculty Award (no. 67507585, D.K.B.). Theoretical work was supported by the Theory of Materials FWP at Lawrence Berkeley National Laboratory, funded by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract no. DE-AC02- 05CH11231 (S.M.G.). K.W. and T.T. acknowledge support from Japan Society for the Promotion of Science KAKENHI (grant nos 19H05790, 20H00354 and 21H05233).

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Authors and Affiliations

  1. Department of Chemistry, University of California, Berkeley, CA, USA

    Isaac M. Craig, Madeline Van Winkle, Catherine Groschner, Kaidi Zhang, Nikita Dowlatshahi & D. Kwabena Bediako

  2. SLAC National Accelerator Laboratory, Stanford, CA, USA

    Ziyan Zhu

  3. International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

  4. Research for Functional Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  5. Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Sinéad M. Griffin

  6. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Sinéad M. Griffin

  7. Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    D. Kwabena Bediako

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Contributions

I.M.C., M.V., C.G. and D.K.B. conceived the study. M.V., C.G., K.Z. and N.D. fabricated the samples. M.V., C.G. and I.M.C. performed the experiments. I.M.C. and Z.Z. performed the continuum simulations using code developed by Z.Z.; I.M.C. developed and implemented the interferometry code (with assistance from C.G.) and analysed the data. T.T. and K.W. provided the hBN crystals. D.K.B. and S.M.G. supervised the work. I.M.C. and D.K.B. wrote the paper with input from all co-authors.

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Correspondence to D. Kwabena Bediako.

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Nature Materials thanks Wu Zhou, Hyobin Yoo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Craig, I.M., Van Winkle, M., Groschner, C. et al. Local atomic stacking and symmetry in twisted graphene trilayers. Nat. Mater. 23, 323–330 (2024). https://doi.org/10.1038/s41563-023-01783-y

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