Energy gaps in the density of states of a graphene buffer layer on silicon carbide: Consideration for the irregularity of layer-substrate coupling

Green’s function and the density of states of epitaxial graphene formed on the surface of a semiconductor are derived in the diagonal approximation. A graphene buffer layer on silicon carbide is considered in detail. It is assumed that, in the buffer layer, there are two types of states, specifically, states weekly and strongly coupled with the substrate. It is shown that, if there is an energy gap in the density of states of the buffer layer, the existence of the gap and its width are defined by the states providing weak graphene-substrate coupling.