The effects of edges on the electronic localization properties of graphene

Abstract

Abstract In this numerically work, we study the effects of edges on the electronic properties of graphene lattices in the quantum Hall regime using a proposed quantity called participation ratio, that is employed to analyze the localization properties of edge states. We use the tight- binding model to include the effects of the magnetic field and disorder. The effect of the edges on the energy levels of the system is studied through Hofstadter’s butterfly-like spectrum. Using the participation ratio and analyzing the contributions of the armchair and zigzag edges separately, we find that there are energy regions where the wave functions are clearly more localized in a specific edge type. The zigzag preferential localization is a reminiscence of the case without magnetic field and the armchair localization which is dependent on the disorder and the strength of the magnetic field, comes from the presence of magnetic field in the system. The results obtained contribute to the understanding of the localization properties of graphene lattices with edges.