Edge stacking dislocations in two-dimensional bilayers with a small lattice mismatch

Incomplete stacking dislocations are predicted to form at edges of the shorter upper layer in two-dimensional hexagonal bilayers upon stretching the longer bottom layer. A concept of the edge Burgers vector is introduced to describe such dislocations by analogy with the Burgers vector of standard bulk dislocations. Analytical solutions for the structure and energy of edge stacking dislocations in bilayer graphene are obtained depending on the magnitude of elongation and angles between the edge Burgers vector, direction of elongation and edge. The barrier for penetration of stacking dislocations inside the bilayer is estimated. The possibilities to measure the barrier to relative motion of graphene layers and strain of graphene on a substrate by observation of edge stacking dislocations are discussed.