Abstract

When a crystal is subjected to a periodic potential, under certain circumstances it can adjust itself to follow the periodicity of the potential, resulting in a commensurate state. Of particular interest are topological defects between the two commensurate phases, such as solitons and domain walls. Here we report a commensurate–incommensurate transition for graphene on top of hexagonal boron nitride (hBN). Depending on the rotation angle between the lattices of the two crystals, graphene can either stretch to adapt to a slightly different hBN periodicity (for small angles, resulting in a commensurate state) or exhibit little adjustment (the incommensurate state). In the commensurate state, areas with matching lattice constants are separated by domain walls that accumulate the generated strain. Such soliton-like objects are not only of significant fundamental interest, but their presence could also explain recent experiments where electronic and optical properties of graphene-hBN heterostructures were observed to be considerably altered.

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Acknowledgements

This work was supported by the European Research Council, Graphene Flagship, Engineering and Physical Sciences Research Council (UK), the Royal Society, US Office of Naval Research, US Air Force Office of Scientific Research, US Army Research Office, the MOST of China (No. 2013CBA01600) and the Körber Foundation. We are grateful to L. Levitov for useful discussions.

Author information

Affiliations

  1. School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK

    • C. R. Woods
    • , L. Britnell
    • , G. L. Yu
    • , A. V. Kretinin
    • , J. Park
    • , L. A. Ponomarenko
    •  & K. S. Novoselov
  2. School of Chemistry and Photon Science Institute, University of Manchester, Oxford Road Manchester, M13 9PL, UK

    • A. Eckmann
    •  & C. Casiraghi
  3. Institute of Physics and University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100190, China

    • R. S. Ma
    • , J. C. Lu
    • , H. M. Guo
    • , X. Lin
    •  & H-J. Gao
  4. Centre for Mesoscience and Nanotechnology, University of Manchester, Manchester M13 9PL, UK

    • Y. Cao
    • , R. V. Gorbachev
    •  & A. K. Geim
  5. Center for Nano-metrology, Korea Research Institute of Standards and Science, 267 Gajeong Ro, Yuseong-Gu Daejeon, 305-340, Republic of Korea

    • J. Park
  6. Institute for Molecules and Materials, Radboud University of Nijmegen, Nijmegen 6525 AJ, The Netherlands

    • M. I. Katsnelson
  7. Institute of Quantum Materials Science, Ekaterinburg 620075, Russia

    • Yu. N. Gornostyrev
  8. National Institute for Materials Science, 1-1 Namiki Tsukuba 305-0044, Japan

    • K. Watanabe
    •  & T. Taniguchi

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Contributions

C.R.W. prepared the samples and did the majority of AFM and Raman experiments. L.B. and A.E. contributed to AFM and Raman experiments. R.S.M., J.C.L., H.M.G. and X.L. did the STM experiments. G.L.Y. and L.A.P. did the transport experiments. Y.C., R.V.G., A.V.K. and J.P. produced experimental samples. M.I.K. and Y.N.G. produced the theoretical analysis. K.W. and T.T. provided hBN. C.C. coordinated and analysed the Raman experiments. H.-J.G. coordinated and analyzed the STM experiments. A.K.G. and K.S.N. initiated and coordinated the work, participated in the experiments, analysed data, and wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to K. S. Novoselov.

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DOI

https://doi.org/10.1038/nphys2954

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