A topologically-derived dislocation theory for twist and stretch moir\'e superlattices in bilayer graphene

TL;DR

This paper introduces a continuum dislocation theory for twist and stretch moire superlattices in bilayer graphene, capturing their structure and energetics without adjustable parameters and matching atomistic simulations.

Contribution

It presents a topologically-derived continuum model that analytically solves for dislocation structures in moire superlattices, incorporating both strain and stacking energy contributions.

Findings

Maximum structure deviation of 6% compared to atomistic simulations

Maximum line energy deviation of 0.019 eV/Angstrom

Successfully predicts structure variation with twist angle and dislocation properties.

Abstract

We develop a continuum dislocation description of twist and stretch moire superlattices in 2D material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moire structure. The approach is based on solving analytically for the structural distortion and displacement fields that satisfy the topological constraints, and which minimize the total energy. The total energy is described by both the strain energy of each individual distorted layer, and a Peierls-Nabarro like interfacial contribution arising from stacking disregistry. The dislocation core emerges naturally within the formalism as a result of the competition between the two contributions. The approach presented here captures the structure and energetics of twist and stretch moire superlattices of dislocations with arbitrary direction and character, without assuming an analytical solution a priori, with no adjustable parameters, while accounting naturally for dislocation-dislocation image interactions. In comparisons to atomistic simulations using classical potentials, the maximum structure deviation is 6%, while the maximum line energy deviation is 0.019 eV/Angstrom. Several applications of our model are shown, including predicting the variation of structure with twist angle, and describing dislocation line tension and junction energies.