Universal features of point defect spectrum in graphene

Abstract

We investigate the electronic structure of localized point defects in two-dimensional graphene. We note that this has been studied in the recent past. Our work is distinguished by its focus on universal features of the point defect spectra. We show that the defect levels converge to three “fixed points” at large defect potentials. In other words the defect levels are “pinned”. We investigate the “pinning”, its robustness and show that it is a consequence of density of states of the host system. We study the localization or otherwise of these “pinned” levels and also of other levels. A critical defect potential is identified. These and other features are studied both using model density of states as well as realistic nearest neighbour and next nearest neighbour tight binding Hamiltonians. We consider both orthogonal as well as non-orthogonal cases. Finally, we discuss future programs of study.