Moir\'e pattern interlayer potentials in van der Waals materials from random-phase approximation calculations

TL;DR

This study uses advanced RPA calculations to accurately model stacking-dependent interlayer interactions in 2D materials like graphene and BN, providing reliable energy difference estimates and phenomenological fits for various properties.

Contribution

It introduces high-level RPA calculations for interlayer potentials in van der Waals materials, demonstrating the reliability of LDA estimates and providing detailed parameterizations.

Findings

LDA and RPA total energies differ significantly, but energy differences are consistent.

Phenomenological fits enable accurate calculation of interlayer properties.

Long-range interactions significantly influence interlayer energetics.

Abstract

Stacking-dependent interlayer interactions are important for understanding the structural and electronic properties in incommensurable two dimensional material assemblies where long-range moir\'e 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 hetero-structures using high-level random-phase approximation (RPA) ab initio calculations. Our results show that although total binding energies within LDA and RPA differ substantially between 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. Parameterisations for all fits are provided.