Stacking in incommensurate graphene/hexagonal-boron-nitride heterostructures based on ab initio study of interlayer interaction

TL;DR

This study uses ab initio calculations to model interlayer interactions in graphene/boron-nitride heterostructures, revealing a simple symmetry-based expression that links physical properties and suggests experimental ways to probe phase transitions.

Contribution

It introduces a highly accurate, symmetry-based approximation for interlayer interactions in graphene/BN systems, simplifying the analysis of their physical properties.

Findings

Interlayer interaction energy depends on relative in-plane position and can be fitted with two parameters.

The approximation allows estimation of properties like Moiré period correction, dislocation width, and shear frequencies.

Proposes experimental observation of phase transition via critical strain measurements.

Abstract

The interlayer interaction in graphene/boron-nitride heterostructures is studied using density functional theory calculations with the correction for van der Waals interactions. It is shown that the use of the experimental interlayer distance allows to describe the potential energy surface at the level of more accurate but expensive computational methods. On the other hand, it is also demonstrated that the dependence of the interlayer interaction energy on the relative in-plane position of the layers can be fitted with high accuracy by a simple expression determined by the system symmetry. The use of only two independent parameters in such an approximation suggests that various physical properties of flat graphene/boron-nitride systems are interrelated and can be expressed through these two parameters. Here we estimate some of the corresponding physical properties that can be accessed experimentally, including the correction to the period of the Moir\'{e} superstructure for the highly incommensurate ground state of graphene/boron-nitride bilayer coming from the interlayer interaction, width of stacking dislocations in slightly incommensurate systems of boron nitride on stretched graphene and shear mode frequencies for commensurate graphene/boron-nitride systems, such as a flake on a layer. We propose that the commensurate-incommensurate phase transition can be observed in boron nitride on stretched graphene and experimental measurements of the corresponding critical strain can be also used to get an insight into graphene/boron-nitride interactions.