Disorder Induced Localized States in Graphene

Abstract

We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is shown that vacancies induce the formation of localized states. When particle-hole symmetry is broken, localized states become resonances close to the Fermi level. We also study the problem of a finite density of vacancies, obtaining the electronic density of states, and discussing the issue of electronic localization in these systems. Our results have also relevance for the problem of disorder in d-wave superconductors.PACS numbers: 81.05. Uw, 71.27.+a, Introduction. The problem of disorder in systems with Dirac fermions has been studied extensively in the last few years in the context of dirty d-wave superconductors [1]. Dirac fermions are also the elementary excitations of the honeycomb lattice at half-filling, equally known as graphene, which is realized in two-dimensional (2D) Carbon based materials with sp 2 bonding. It is well-known that disorder is ubiquitous in graphene and graphite (which is produced by stacking graphene sheets) and its effect on the electronic structure has been studied extensively [2,3,4,5,6,7,8,9,10,11,12,13]. It has been shown recently [14] that the interplay of disorder and electron-electron interactions is fundamental for the understanding of recent experiments in graphene devices [15]. Furthermore, experiments reveal that ferromagnetism is generated in heavily disordered graphite samples [16,17,18,19,20], but the understanding of the interplay of strong disorder and electron-electron interactions in these systems is still in its infancy. Different mechanisms for ferromagnetism in graphite have been proposed and they are either based on the nucleation of ferromagnetism around extended defects such as edges [2,8,12,13] or due to exchange interactions originating from unscreened Coulomb interactions [21]. Therefore, the understanding of the nature of the electronic states in Dirac fermion systems with strong disorder is of the utmost interest.In the following, we analyze in detail states near the Fermi energy induced by vacancies in a tight-binding model for the electronic states of graphene planes. We show that single vacancies in a graphene plane generate localized states which are sensitive to the presence of particle-hole symmetry breaking. Moreover, a finite density of such defects leads to strong changes in the local and averaged electronic Density Of States (DOS) with the creation of localized states at the Dirac point.The model. We consider a single band model described by the Hamiltonian:

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