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Cryogenic nano-imaging of second-order moiré superlattices

Nature Materials (2024)Cite this article

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Abstract

Second-order superlattices form when moiré superlattices with similar periodicities interfere with each other, leading to larger superlattice periodicities. These crystalline structures are engineered using two-dimensional materials such as graphene and hexagonal boron nitride, and the specific alignment plays a crucial role in facilitating correlation-driven topological phases. Signatures of second-order superlattices have been identified in magnetotransport experiments; however, real-space visualization is still lacking. Here we reveal the second-order superlattice in magic-angle twisted bilayer graphene closely aligned with hexagonal boron nitride through electronic transport measurements and cryogenic nanoscale photovoltage measurements and evidenced by long-range periodic photovoltage modulations. Our results show that even minuscule strain and twist-angle variations as small as 0.01° can lead to drastic changes in the second-order superlattice structure. Our real-space observations, therefore, serve as a ‘magnifying glass’ for strain and twist angle and can elucidate the mechanisms responsible for the breaking of spatial symmetries in twisted bilayer graphene.

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Fig. 1: Nanoscale photovoltage measurements of MATBG/hBN SOSLs at T = 10 K.
Fig. 2: Gate and temperature responses of the observed photovoltage features and broken inversion symmetry.
Fig. 3: Electronic transport measurements.
Fig. 4: Calculation of second-order superlattice properties.
Fig. 5: Real-space maps of the SOSL as a function of twist angle and strain magnitude.

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The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

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The code that supports the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

F.H.L.K. acknowledges financial support from the Government of Catalonia through the SGR grant, and from the Spanish Ministry of Economy and Competitiveness through the Severo Ochoa Programme for Centres of Excellence in R&D (no. SEV-2015-0522) and Explora Ciencia (no. FIS2017-91599-EXP). F.H.L.K. also acknowledges support from the Fundacio Cellex Barcelona, Generalitat de Catalunya, through the CERCA program and the Mineco grant Plan Nacional (no. FIS2016-81044-P) and the Agency for Management of University and Research Grants (AGAUR) (no. 2017-SGR-1656). Furthermore, the research leading to these results has received funding from the European Union’s Horizon 2020 programme under grant agreement nos. 785219 (Graphene Flagship Core2), 881603 (Graphene Flagship Core3) and 820378 (Quantum Flagship). This work was supported by the ERC under grant agreement no. 726001 (TOPONANOP). P.S. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant no. 754510. N.C.H.H. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 665884. K.W. and T.T. acknowledge support from JSPS KAKENHI (grant nos. 19H05790, 20H00354 and 21H05233). This project has received funding from the ‘Presidencia de la Agencia Estatal de Investigación’ within the PRE2020-094404 predoctoral fellowship.

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Authors and Affiliations

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

    Niels C. H. Hesp, Sergi Batlle-Porro, Roshan Krishna Kumar, Hitesh Agarwal, David Barcons Ruiz, Hanan Herzig Sheinfux, Petr Stepanov & Frank H. L. Koppens

  2. Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

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

    Takashi Taniguchi

  4. Department of Physics and Astronomy, University of Notre Dame, Notre Dame, IN, USA

    Petr Stepanov

  5. Stavropoulos Center for Complex Quantum Matter, University of Notre Dame, Notre Dame, IN, USA

    Petr Stepanov

  6. ICREA—Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain

    Frank H. L. Koppens

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Contributions

F.H.L.K. conceived the experiment. N.C.H.H., S.B.-P. and P.S. performed the near-field experiments on a system optimized by N.C.H.H., D.B.R. and H.H.S. Transport experiments were performed by P.S. on a system built by R.K.K. The sample was fabricated by P.S. using a contact recipe developed by H.A. and with hBN crystals provided by K.W. and T.T. The results were analysed and interpreted by N.C.H.H. and P.S. using a model developed by N.C.H.H. The manuscript was written by P.S., N.C.H.H. and F.H.L.K. with input from all authors. F.H.L.K. supervised the work.

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Correspondence to Petr Stepanov or Frank H. L. Koppens.

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Hesp, N.C.H., Batlle-Porro, S., Krishna Kumar, R. et al. Cryogenic nano-imaging of second-order moiré superlattices. Nat. Mater. (2024). https://doi.org/10.1038/s41563-024-01993-y

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