Vacancies in epitaxial graphene

The coherent-potential method is used to consider the problem of the influence of a finite concentration of randomly arranged vacancies on the density of states of epitaxial graphene. To describe the density of states of the substrate, simple models (the Anderson model, Haldane-Anderson model, and parabolic model) are used. The electronic spectrum of free single-sheet graphene is considered in the low-energy approximation. Charge transfer in the graphene-substrate system is discussed. It is shown that, in all cases, the density of states of epitaxial graphene decreases proportionally to the vacancy concentration. At the same time, the average charge transferred from graphene to the substrate increases.