Interlayer coupling in rotationally faulted multilayer graphenes

This article reviews progress in the theoretical modelling of the electronic structure of rotationally faulted multilayer graphenes. In these systems the crystallographic axes of neighboring layers are misaligned so that the layer stacking does not occur in the Bernal structure observed in three dimensional graphite and frequently found in exfoliated bilayer graphene. Notably, rotationally faulted graphenes are commonly found in other forms of multilayer graphene including epitaxial graphenes thermally grown on ${\rm SiC \, (000 \bar 1)}$, graphenes grown by chemical vapor deposition, folded mechanically exfoliated graphenes, and graphene flakes deposited on graphite. Rotational faults are experimentally associated with a strong reduction of the energy scale for coherent single particle interlayer motion. The microscopic basis for this reduction and its consequences have attracted significant theoretical attention from several groups that are highlighted in this review.