Even with a thickness of just one atomic layer, graphene grown on a crystalline substrate can be understood as a thin film that has exceeded the critical thickness for formation of interface misfit dislocations.  For the case of monolayer graphene on a metal substrate, or for the case of twisted bilayer graphene, the resulting interface misfit dislocation networks are more readily recognized as moir√© patterns.  Understanding moir√© patterns as geometrically necessary dislocations is a useful framework for understanding the mechanics of 2D material systems, and it facilitates the explanation of a variety of experimental observations.  One such example, presented here, is in the static and dynamic behavior of finite 2D material flakes and their spontaneous motion on a crystalline substrate.  Finally, the dislocation framework has implications for the emerging field of ‚Äúmoir√© engineering‚Äù, whereby one controls the interface misfit dislocation structure in order to tailor the electrical properties of the system. 

Graphene on a crystalline substrate: when a single monolayer exceeds the critical thickness

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