Structure and energetics of interlayer dislocations in bilayer graphene

We present a general hybrid model based upon the continuum generalized Peierls-Nabarro model (with density functional theory parametrization) to describe interlayer dislocations in bilayer systems. In this model, the bilayer system is divided into two linear elastic 2D sheets. The strains in each sheet can be relaxed by both elastic in-plane deformation and out-of-plane buckling; this deformation is described via classical linear elastic thin plate theory. The interlayer bonding between these two sheets is described by a three-dimensional generalized stacking-fault energy (GSFE) determined from first principle calculations and based upon the relative displacement between the sheets. The structure and energetics of various interlayer dislocations in bilayer graphene was determined by minimizing the elastic and bonding energy with respect to all displacements. The dislocations break into partials, and pronounced buckling is observed at the partial dislocation locations to relax the strain induced by their edge components. The partial dislocation core width is reduced by buckling. An analytical model is also developed based upon the results obtained in numerical simulation. We develop an analytical model for the bilayer structure and energy and show that these predictions are in excellent agreement with the numerical results.