Moir{\'e} patterns as a probe of interplanar interactions: graphene on h-BN

TL;DR

This study uses atomistic modeling of moiré patterns in graphene on h-BN to understand interlayer interactions and strain distributions, revealing how the ratio of C-N to C-B interactions influences the pattern and providing insights into dispersive forces in van der Waals heterostructures.

Contribution

It demonstrates that moiré patterns can serve as a probe for interplanar interactions and strain distributions in graphene/h-BN heterostructures, highlighting the importance of C-B and C-N interaction ratios.

Findings

Agreement with experimental data requires C-B interactions to be at least twice weaker than C-N interactions.

Strain distribution varies with misorientation angle, indicating a commensurate-incommensurate transition.

Moiré patterns reflect the potential energy surface, enabling study of dispersive forces.

Abstract

By atomistic modeling of moir{\'e} patterns of graphene on a substrate with a small lattice mismatch, we find qualitatively different strain distributions for small and large misorientation angles, corresponding to the commensurate-incommensurate transition recently observed in graphene on hexagonal BN. We find that the ratio of C-N and C-B interactions is the main parameter determining the different bond lengths in the center and edges of the moir{\'e} pattern. Agreement with experimental data is obtained only by assuming that the C-B interactions are at least twice weaker than the C-N interactions. The correspondence between the strain distribution in the nanoscale moir{\'e} pattern and the potential energy surface at the atomic scale found in our calculations, makes the moir{\'e} pattern a tool to study details of dispersive forces in van der Waals heterostructures.