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Commensurate–incommensurate transition in graphene on hexagonal boron nitride

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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Figure 1: Schematic representation of the moiré pattern of graphene (red) on hBN (blue).
Figure 2: Experimental observation of moiré patterns for graphene-on-hBN samples with different relative orientation angles.
Figure 3: STM measurements on one of our fully aligned graphene-on-hBN samples.
Figure 4: Raman measurements on aligned and misaligned graphene on hBN samples.
Figure 5: Transport measurements and estimation of a gap on encapsulated and non-encapsulated samples.

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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.

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Authors

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.

Corresponding author

Correspondence to K. S. Novoselov.

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The authors declare no competing financial interests.

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Woods, C., Britnell, L., Eckmann, A. et al. Commensurate–incommensurate transition in graphene on hexagonal boron nitride. Nature Phys 10, 451–456 (2014). https://doi.org/10.1038/nphys2954

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