Interlayer torsional sliding and strain localization in bilayer graphene

Twisted bilayer graphene can demonstrate extraordinary optical and electrical characteristics due to its interlayer interactions. The strong coupling of normal and tangential van der Waals interactions at the interface results in inhomogeneous interlayer deformations and further changes the bilayer graphene's physical properties. Herein, theoretical and numerical models are established to study the torsional deformation behaviour of twisting a graphene flake over a rigid graphene substrate. It is found that in-plane deformations have significant influences on the interlayer potential energy density of AA stacking, but seldom affect other stacked domains. The deformation process is thus approximated by first twisting the graphene flake rigidly, and then relaxing the rigid constraints. The bilayer graphene system minimizes its energy by reducing (enlarging) the size of high-energy (low-energy) domains through additional rotations. The additional angles of the graphene flake are derived analytically based on a mechanical model following the principle of minimum potential energy. Results show that the influences of graphene film deformations get significant at small-twist-angles (typically less than 2 degrees). This work reveals the torsional deformation evolution mechanism of bilayer graphene and provides beneficial guidance on achieving intriguing physical properties.