Relaxation and domain wall structure of bilayer moire systems

TL;DR

This paper develops a continuum elastic model for bilayer moire systems, analyzing their domain wall structures and providing asymptotic estimates that explain observed patterns at small twist angles.

Contribution

It introduces a new continuum model incorporating intralayer and interlayer energies, and rigorously estimates domain wall structures and gradient norms in twisted bilayers.

Findings

Large alternating regions separated by domain walls are predicted.

Asymptotic estimates for domain wall structures are derived.

Gradient norms scale inversely with twist angle, explaining domain wall formation.

Abstract

Moire patterns result from setting a 2D material such as graphene on another 2D material with a small twist angle or from the lattice mismatch of 2D heterostructures. We present a continuum model for the elastic energy of these bilayer moire structures that includes an intralayer elastic energy and an interlayer misfit energy that is minimized at two stackings (disregistries). We show by theory and computation that the displacement field that minimizes the global elastic energy subject to a global boundary constraint gives large alternating regions of one of the two energy-minimizing stackings separated by domain walls. We derive a model for the domain wall structure from the continuum bilayer energy and give a rigorous asymptotic estimate for the structure. We also give an improved estimate for the L2-norm of the gradient on the moire unit cell for twisted bilayers that scales at most inversely linearly with the twist angle, a result which is consistent with the formation of one-dimensional domain walls with a fixed width around triangular domains at very small twist angles.