Origin of the vortex displacement field in twisted bilayer graphene

A model description of patterns of atomic displacements in twisted bilayer systems has been proposed. The model is based on the consideration of several dislocation ensembles, employing a language that is widely used for grain boundaries and film/substrate systems. We demonstrate explicitly how the dislocation language relates to vortex lattice motives found in experiment and simulations. We show that three ensembles of parallel screw dislocations are sufficient both to describe the rotation of the layers as a whole, and for the vortexlike displacements resulting from elastic relaxation. The results give a clear explanation of the observed features of the structural state such as vortices, accompanied by alternating stacking.