On the density of states of disordered epitaxial graphene

The study is concerned with two types of disordered epitaxial graphene: (i) graphene with randomly located carbon vacancies and (ii) structurally amorphous graphene. The former type is considered in the coherent potential approximation, and for the latter type, a model of the density of states is proposed. The effects of two types of substrates, specifically, metal and semiconductor substrates are taken into account. The specific features of the density of states of epitaxial graphene at the Dirac point and the edges of the continuous spectrum are analyzed. It is shown that vacancies in epitaxial graphene formed on the metal substrate bring about logarithmic nulling of the density of states of graphene at the Dirac point and the edges of the continuous spectrum. If the Dirac point corresponds to the middle of the band gap of the semiconductor substrate, the linear trend of the density of states to zero in the vicinity of the Dirac point in defect-free graphene transforms into a logarithmic decrease in the presence of vacancies. In both cases, the graphene-substrate interaction is assumed to be weak (quasi-free graphene). In the study of amorphous epitaxial graphene, a simple model of free amorphous graphene is proposed as the initial model, in which account is taken of the nonzero density of states at the Dirac point, and then the interaction of the graphene sheet with the substrate is taken into consideration. It is shown that, near the Dirac point, the quadratic behavior of the density of states of free amorphous graphene transforms into a linear dependence for amorphous epitaxial graphene. In the study, the density of states of free graphene corresponds to the low-energy approximation of the electron spectrum.