Relaxation of moir\'e patterns for slightly misaligned identical lattices: graphene on graphite

TL;DR

This study investigates how atomic relaxation influences moiré patterns in slightly misaligned graphene layers on graphite, revealing complex reconstructed structures that significantly impact electronic properties and deviate from simple sinusoidal models.

Contribution

It provides large-scale atomistic simulations showing the detailed atomic relaxation effects on moiré patterns in twisted graphene systems.

Findings

Reconstructed moiré structures form superlattices of hot spots with vortex-like displacements.

Out-of-plane displacements increase as misorientation angle decreases.

Structures deviate from sinusoidal modulation at angles below ~1°.

Abstract

We study the effect of atomic relaxation on the structure of moir\'e patterns in twisted graphene on graphite and double layer graphene by large scale atomistic simulations. The reconstructed structure can be described as a superlattice of `hot spots' with vortex-like behaviour of in-plane atomic displacements and increasing out-of-plane displacements with decreasing angle. These lattice distortions affect both scalar and vector potential and the resulting electronic properties. At low misorientation angles (<$\sim$1$^\circ$) the optimized structures deviate drastically from the sinusoidal modulation which is often assumed in calculations of the electronic properties. The proposed structure might be verified by scanning probe microscopy measurements.