Two-dimensional material bilayers consisting of graphene, h-BN, and transition metal dichalcogenides like MoS2, are emerging as a platform for an exciting new class of devices based on twistronics, in which relative rotation between the layers can endow the system with exotic electronic properties.  The origin of these interesting properties is in the moir√© patterns associated with periodic regions of incommensurability between the layers.  Here we describe the energetics of the bilayer structure and their moir√© patterns, which explain the experimentally observed spontaneous small-angle rotations between finite-sized flakes and much larger substrates.  This effect can be understood in the context of arrays of van der Waals (vdW) dislocations, or geometrically necessary dislocations that result from misalignment of the two layers.  This effect has implications in the design of ‚Äúmagic-angle‚Äù bilayer graphene structures exhibiting superconductivity, and in selection of desirable polycrystalline microstructures in the CVD growth of 2D materials.

Stability of finite-sized flakes in bilayer 2D material systems

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