Anomalous confined electron states in graphene superlattices

Abstract

We show that periodic scalar potentials can induce the localization of some electronic states in graphene. Particularly, localized states are found at energies outside the potential variation range and embedded in the continuum spectrum of delocalized ones. The picture of the connection of wave functions with typical symmetries defined in relevant-edge nanoribbons is employed to explain the formation of the electronic structure and to characterize/classify eigen-states in graphene superlattices.