van der Waals bilayer energetics: Generalized stacking-fault energy of graphene, boron nitride, and graphene/boron nitride bilayers

The structure, thermodynamics, and band gaps in graphene/graphene, boron nitride/boron nitride, and graphene/boron nitride bilayers are determined using several different corrections to first-principles approaches to account for the dispersion interactions. While the density functional dispersion correction, van der Waals density functional, meta--generalized gradient approximation, and adiabatic fluctuation-dissipation theorem methods (ACFDT-RPA) all lead to qualitatively similar predictions, the best accuracy is obtained through the application of the computationally expensive ACFDT-RPA method. We present an accurate ACFDT-RPA-based method to determine bilayer structure, generalized stacking-fault energy (GSFE), and band gaps as a function of the relative translation states of the two layers. The GSFE data clearly identify all of the stable and metastable bilayer translations as well as the barriers between them. This is key for predicting the sliding, formation, and adhesion energies for homo- and hetero-bilayers, as well as for the determination of defects in such multilayer van der Waals systems. These, in turn, provide an accurate approach for determining and manipulating the spatial variation of electronic structure.