Lattice Relaxation in Moir\'e Heterobilayers

TL;DR

This paper presents an analytical theory for lattice relaxation in twisted moiré heterobilayers, incorporating various physical effects and validated against numerical solutions, with implications for understanding buckling instabilities.

Contribution

The authors develop a self-consistent analytical framework for lattice relaxation in moiré heterobilayers, including effects of mismatch, strain, and elastic properties, validated by numerical comparisons.

Findings

Analytical expressions match numerical solutions well for relevant parameters.

Heterobilayers can exhibit buckling instability near alignment due to strain.

The framework simplifies incorporating lattice relaxation effects in realistic models.

Abstract

We develop an analytical theory for lattice relaxation in twisted moir\'e heterobilayers, accounting for lattice mismatch, twist, external biaxial heterostrain, and different elastic constants. Starting from continuum elasticity, we derive the self-consistent equations for the in-plane displacement fields and obtain simple perturbative expressions for the layer-resolved in-plane displacement fields induced by lattice relaxation. We apply our theory to graphene on hBN and representative 2H transition metal dichalcogenide heterobilayers, including MoTe$_2$/WSe$_2$ and WSe$_2$/WS$_2$. Our analytical results agree very well with full numerical solutions over experimentally relevant parameters. We further show that heterobilayers can exhibit a buckling instability near alignment, driven by compressive in-plane strain due to moir\'e relaxation. Our results provide a simple theoretical framework for incorporating lattice relaxation in realistic moir\'e heterostructures.