Adhesion and Reconstruction of Graphene/Hexagonal Boron Nitride Heterostructures: A Quantum Monte Carlo Study

TL;DR

This study uses quantum Monte Carlo methods to accurately analyze interlayer adhesion, relaxation, and electronic properties of graphene/hBN heterostructures, revealing insights into moiré patterns, minibands, and stable layered configurations.

Contribution

It provides a quantum Monte Carlo based calculation of adhesion potentials and predicts the formation of a new stable layered crystal with unique electronic properties.

Findings

Adhesion potential well described by Lennard-Jones parameters.

Moiré pattern period depends on hBN misalignment angle.

Stable layered structure predicted for alternating graphene/hBN stacks.

Abstract

We investigate interlayer adhesion and relaxation at interfaces between graphene and hexagonal boron nitride (hBN) monolayers in van der Waals heterostructures. The adhesion potential between graphene and hBN is calculated as a function of local lattice offset using diffusion quantum Monte Carlo methods, which provide an accurate treatment of van der Waals interactions. Combining the adhesion potential with elasticity theory, we determine the relaxed structures of graphene and hBN layers at interfaces, finding no metastable structures. The adhesion potential is well described by simple Lennard-Jones pair potentials that we parameterize using our quantum Monte Carlo data. Encapsulation of graphene between near-aligned crystals of hBN gives rise to a moir\'{e} pattern whose period is determined by the misalignment angle between the hBN crystals superimposed over the moir\'{e} superlattice previously studied in graphene on an hBN substrate. We model minibands in such supermoir\'{e} superlattices and find them to be sensitive to a 180$^\circ$ rotation of one of the encapsulating hBN crystals. We find that monolayer and bilayer graphene placed on a bulk hBN substrate and bulk hBN/graphene/bulk hBN systems do not relax to adopt a common lattice constant. The energetic balance is much closer for free-standing monolayer graphene/hBN bilayers and hBN/graphene/hBN trilayers. The layers in an alternating stack of graphene and hBN are predicted to strain to adopt a common lattice constant and hence we obtain a new, stable three-dimensional crystal with a unique electronic structure.