Relaxation and Domain Formation in Incommensurate 2D Heterostructures

TL;DR

This paper introduces a configuration space approach for efficiently calculating mechanical relaxation patterns in incommensurate 2D bilayers, enabling analysis of aperiodic structures without supercell approximations.

Contribution

The authors develop a continuum model in configuration space that accurately predicts relaxations in 2D heterostructures, including small-angle twisted bilayers, without relying on empirical atomistic potentials.

Findings

Efficient computation of relaxations at twist angles as small as 0.05°

Applicable to various 2D materials like graphene and MoS₂

Provides insights into domain formation in nearly-aligned bilayers

Abstract

We introduce configuration space as a natural representation for calculating the mechanical relaxation patterns of incommensurate two-dimensional (2D) bilayers, bypassing supercell approximations to encompass aperiodic relaxation patterns. The approach can be applied to a wide variety of 2D materials through the use of a continuum model in combination with a generalized stacking fault energy for interlayer interactions. We present computational results for small-angle twisted bilayer graphene and molybdenum disulfide (MoS$_2$), a representative material of the transition metal dichalcogenide (TMDC) family of 2D semiconductors. We calculate accurate relaxations for MoS$_2$ even at small twist-angle values, enabled by the fact that our approach does not rely on empirical atomistic potentials for interlayer coupling. The results demonstrate the efficiency of the configuration space method by computing relaxations with minimal computational cost for twist angles down to $0.05^\circ$, which is smaller than what can be explored by any available real space techniques. We also outline a general explanation of domain formation in 2D bilayers with nearly-aligned lattices, taking advantage of the relationship between real space and configuration space.