Moiré-pattern interlayer potentials in van der Waals materials in the random-phase approximation

Stacking-dependent interlayer interactions are important for understanding the structural and electronic properties in incommensurable two-dimensional material assemblies where long-range moiré patterns arise due to small lattice constant mismatch or twist angles. Here we study the stacking-dependent interlayer coupling energies between graphene (G) and hexagonal boron nitride (BN) homo- and heterostructures using high-level random-phase approximation (RPA) ab initio calculations. Our results show that although total binding energies within LDA and RPA differ substantially by a factor of 200%-400%, the energy differences as a function of stacking configuration yield nearly constant values with variations smaller than 20%, meaning that LDA estimates are quite reliable. We produce phenomenological fits to these energy differences, which allows us to calculate various properties of interest including interlayer spacing, sliding energetics, pressure gradients, and elastic coefficients to high accuracy. The importance of long-range interactions (captured by RPA but not LDA) on various properties is also discussed. Parametrizations for all fits are provided.