Numerical studies of confined states in rotated bilayers of graphene

Rotated graphene multilayers form a new class of graphene-related systems with electronic properties that drastically depend on the rotation angles. It has been shown that bilayers behave like two isolated graphene planes for large rotation angles. For smaller angles, states in the Dirac cones belonging to the two layers interact resulting in the appearance of two Van Hove singularities. States become localized as the rotation angle decreases and the two Van Hove singularities merge into one peak at the Dirac energy. Here we go further and consider bilayers with very small rotation angles. In this case, well-defined regions of AA stacking exist in the bilayer supercell and we show that states are confined in these regions for energies in the [$\ensuremath{-}{\ensuremath{\gamma}}_{t}$, $+{\ensuremath{\gamma}}_{t}$] range with ${\ensuremath{\gamma}}_{t}$ the interplane mean interaction. As a consequence, the local densities of states show discrete peaks for energies different from the Dirac energy.