Toward Moir\'e engineering in 2D materials via dislocation theory

TL;DR

This paper introduces a dislocation theory-based framework to understand and engineer Moiré patterns in 2D materials, linking mechanics and electronic structure, and providing computational tools for predicting complex patterns and defects.

Contribution

It presents a novel geometrical description of van der Waals dislocations and a computational scheme to simulate Moiré patterns, unifying mechanical and electronic aspects in 2D materials.

Findings

Moiré patterns can be modeled as dislocation arrays.

The framework predicts all observed Moiré patterns in 2D systems.

Linear defects in Moiré space act as topological states.

Abstract

We present a framework that explains the strong connection in 2D materials between mechanics and electronic structure, via dislocation theory. Within this framework, Moir\'e patterns created by layered 2D materials may be understood as dislocation arrays, and vice versa. The dislocations are of a unique type that we describe as van der Waals dislocations, for which we present a complete geometrical description, connected to both stretch and twist Moir\'e patterns. A simple computational scheme, which reduces the complexity of the electronic interaction between layers in order to make the problem computationally tractable, is introduced to simulate these dislocation arrays, allowing us to predict and explain all of the observed Moir\'e patterns in 2D material systems within a unique framework. We extend this analysis as well to defects in Moir\'e patterns, which have been reported recently, and which are the result of defects of the same symmetry in the constituent 2D material layers. Finally, we show that linear defects in the Moir\'e space can be viewed as unidimensional topological states, and can be engineered using our framework