Phase Field Crystal Methods for Bilayer Graphene

Abstract

Bilayer graphene has been a subject of intense study in recent years. We extend a structural phase field crystal method to include an external potential based on the generalized stacking-fault energy that accounts for the effect from a bottom layer of graphene. Both of the favored stacking variants are found with randomly generated initial phase fields. Using the width of the boundaries between different stacking variants as a function of the interactions between the two layers, we quantify the exact strength of the external potential by comparing the phase field crystal simulations with the results from atomistic simulation. We simulate a circular grain of one stacking phase enclosed by the other and find that, depending on the initial phase field, the center domain may shrink to form a uniform stacking phase, or may evolve to a relaxed state of a hexagon region or a triangular region that at each vertex the graphene structure is defected.