Designing Moir\'e Patterns by Strain

TL;DR

This paper explores how strain influences moiré pattern formation in twisted two-dimensional materials, revealing that strain can be used to engineer diverse moiré geometries and affect their electronic properties.

Contribution

It demonstrates that strain, combined with twist, can generate a wide variety of moiré patterns and provides a theoretical framework for designing such patterns through strain engineering.

Findings

Strain can produce virtually any moiré geometry in honeycomb lattices.

The moiré Brillouin zone shape depends on the strain-induced moiré vectors.

Strain tends to suppress flat moiré bands, affecting electronic properties.

Abstract

Experiments conducted on two-dimensional twisted materials have revealed a plethora of moir\'e patterns with different forms and shapes. The formation of these patterns is usually attributed to the presence of small strains in the samples, which typically arise during their fabrication. In this work we find that the superlattice structure of such systems actually depends crucially on the interplay between twist and strain. For systems composed of honeycomb lattices, we show that this can lead to the formation of practically any moir\'e geometry, even if each lattice is only slightly distorted. As a result, we show that under strain the moir\'e Brillouin zone is not a stretched irregular hexagon, but rather a primitive cell that changes according to the geometry of the strained moir\'e vectors. We identify the conditions for the formation of hexagonal moir\'e patterns arising solely due to shear or biaxial strain, thus opening the possibility of engineering moir\'e patterns solely by strain. Moreover, we study the electronic properties in such moir\'e patterns and find that the strain tends to suppress the formation of the flat moir\'e bands, even in the strain-induced hexagonal patterns analogous to those obtained by the twist only. Our work explains the plethora of moir\'e patterns observed in experiments, and provides a solid theoretical foundation from which one can design moir\'e patterns by strain.