Elastic properties of moir\'e lattices in epitaxial two-dimensional materials

TL;DR

This paper develops a continuous+atomistic elastic membrane model to study out-of-plane deformations in moiré patterns of 2D materials, revealing how mechanical energies influence moiré wavelength and wrinkle formation.

Contribution

It introduces a novel elastic membrane approach that accounts for out-of-plane deformations, advancing understanding of moiré pattern mechanics in 2D materials.

Findings

Elastic energies can compete with adhesion energy in 2D moiré systems.

Out-of-plane deformations influence moiré wavelength selection.

Wrinkle formation results from the interplay of bending and adhesion energies.

Abstract

Unlike conventional two-dimensional (2D) semiconductor superlattices, moir\'{e} patterns in 2D materials are flexible and their electronic, magnetic, optical, and mechanical properties depend on their topography. Within a continuous+atomistic theory treating 2D materials as crystalline elastic membranes, we abandon the flat-membrane scenario usually assumed for these materials and address out-of-plane deformations. We confront our predictions to experimental analyses on model systems, epitaxial graphene, and MoS$_2$ on metals and reveal that compression/expansion and bending energies stored in the membrane can compete with adhesion energy, leading to a subtle moir\'{e} wavelength selection and the formation of wrinkles.