Atomic Structures of Multiply-Folded Graphene Layers on Flat Substrates

Abstract

We have systematically studied the energetics of multiply-folded graphene layers on flat substrates, by atomistic-scale simulations using the empirical potentials proposed by Tersoff and Lennard-Jones. We find that the atomic structures of doubly-folded graphene layers consist of 2 motifs (bulge and root) for small-sized folds, and 3 motifs (bulge, root, and stacked-layer) for large-sized folds. The transition between them is caused by the competition between the adhesion-energy gain due to layer stacking and the elastic-energy loss associated with membrane distortion. Such a qualitative change in the atomic structure with increasing the fold size is a noteworthy feature of multiple folding which has not been addressed. We also calculate four-fold or more folding of graphene layers, successfully explaining an atomic force microscopy image reported in an experiment. Interspaces of different sizes and Moiré patterns appear in the atomic structures of the folds, which we believe can be exploited to generate intercalation compounds and electron states with favorable properties.