Time-lapsed graphene moiré superlattices on Cu(1 1 1)

Abstract

We report classical molecular dynamics simulations (CMD) of the moiré superlattice of graphene on Cu(1 1 1) using a new parameterized Abell–Tersoff potential for the graphene/Cu(1 1 1) interface fitted in this paper to nonlocal van der Waals density functional theory calculations. The interfacial force field with time-lapsed CMD provides superlattices in good quantitative agreement with the available experimental results. The long range coincidence supercells with nonequivalent moiré hills have also been identified and analyzed. Spot profile analysis reveals that the moiré spots are inequivalent over large areas, and their heights are randomly distributed. This result is in accordance with recent atomic force microscopy studies. Our simulations also shed light on the transient dynamics of the moiré superlattice in atomic detail. The moiré superlattice exhibits a pattern which is dynamical rather than statically pinned to the support, and can be observed mostly via time-lapsing. The instantaneous snapshots of the periodic moiré pattern at low temperature are already weakly disordered, lacking the apparent sharpness of the time-averaged pattern and of the scanning tunneling microscopy images. This suggests the existence of competition of orders—between a static (first-order) moiré superstructure and a dynamical (second-order) moiré superstructure.