Density functional calculations on the intricacies of Moiré patterns on graphite

Abstract

Scanning tunneling microscopy (STM) imaging has detected a wealth of puzzling features on the surface of highly oriented pyrolytic graphite, among them, anomalously large superperiodicities, called Moir\'e patterns, caused by the lattice-mismatched top layer of graphite. Exactly, the top graphene layer rotates with respect to the graphite substrate. Such rotation gives rise to different types of local stackings in the different surface graphite regions. As STM mapping is highly dependent on the differences of local density of states of the graphite surface at the Fermi level, variations in brightness differentiate graphite regions with different local stackings. Bright areas (visible graphite areas) correspond to $AABABAB\dots{}$ local graphite stackings, whereas dark areas (hidden graphite areas) to $BABABAB\dots{}$ or $CABABAB\dots{}$ ones. We have programmed an algorithm which first built systematically the whole range of Moir\'e structures and afterwards quantified the percentages of the different local graphite stackings. Finally, periodic density functional theory calculations have been performed on a selection of Moir\'e structures in order to draw the energy profile of the rotation between two graphene layers.