Restriction of macroscopic structural superlubricity due to structure relaxation by the example of twisted graphene bilayer

TL;DR

This study investigates how structure relaxation affects the potential energy surface and static friction in twisted graphene bilayers, revealing that relaxation can significantly increase friction for larger moiré patterns and alter PES symmetry.

Contribution

It demonstrates that structure relaxation can dominate static friction in large moiré systems and shows how PES symmetry changes due to relaxation, advancing understanding of superlubricity limits.

Findings

Relaxation increases PES corrugations for large unit cells.

Structure relaxation can change PES from maxima to minima.

Static friction can be dominated by relaxation effects in certain conditions.

Abstract

The effect of structure relaxation on the potential energy surface (PES) of interlayer interaction of twisted graphene bilayer is studied for a set of commensurate moir\'e systems using the registry-dependent empirical potential of Kolmogorov and Crespi. It is found that the influence of structure relaxation on the amplitude of PES corrugations (determining static friction) depends on the unit cell size (or related twist angle) of the moir\'e system. For moir\'e systems with the smallest unit cells, the amplitudes of PES corrugations calculated with and without account of structure relaxation are approximately the same. However, for large unit cell sizes, the structure relaxation can lead to an increase of PES corrugations by orders of magnitude. This means that structure relaxation can provide the main contribution into the static friction of a superlubric system under certain conditions (such as the contact size and twist angle). Moreover, the change of the PES type because of structure relaxation from a trigonal lattice of maxima to a trigonal lattice of minima is observed for the systems with the moir\'e patterns (5,1) and (5,3). Based on the results obtained, possible crossovers between static friction modes taking place upon changing the twist angle in a macroscopic superlubric system consisting of identical layers are discussed. Additionally it is shown that the PES for relaxed structures can still be approximated by the first Fourier harmonics compatible with symmetries of twisted layers analogously to the PES for rigid layers.