  When a crystal is subjected to a periodic potential, under certain
circumstances (such as when the period of the potential is close to the crystal
periodicity; the potential is strong enough, etc.) it might adjust itself to
follow the periodicity of the potential, resulting in a, so called,
commensurate state. Such commensurate-incommensurate transitions are ubiquitous
phenomena in many areas of condensed matter physics: from magnetism and
dislocations in crystals, to vortices in superconductors, and atomic layers
adsorbed on a crystalline surface. Of particular interest might be the
properties of topological defects between the two commensurate phases:
solitons, domain walls, and dislocation walls. Here we report a
commensurate-incommensurate transition for graphene on top of hexagonal boron
nitride (hBN). Depending on the rotational angle between the two hexagonal
lattices, graphene can either stretch to adjust to a slightly different hBN
periodicity (the commensurate state found for small rotational angles) or
exhibit little adjustment (the incommensurate state). In the commensurate
state, areas with matching lattice constants are separated by domain walls that
accumulate the resulting strain. Such soliton-like objects present significant
fundamental interest, and their presence might explain recent observations when
the electronic, optical, Raman and other properties of graphene-hBN
heterostructures have been notably altered.
