On the specific features of the density of states of epitaxial graphene formed on metal and semiconductor substrates

Analytical expressions for the local densities of states of epitaxial graphene formed on metal and semiconductor substrates are derived on unified grounds. The conditions of strong and weak graphene-substrate coupling are considered. It is shown that, in the case of strong coupling (the interaction of carbon atoms of graphene with the substrate is much stronger than that of carbon atoms with each other), the local density of states of graphene is close to the density of states of an individual carbon adatom on both metal and semiconductor substrates. In the opposite case of weak graphene-(semiconductor substrate) coupling (the interaction of carbon atoms of graphene with the substrate is much weaker than that of carbon atoms with each other), there is no gap in the local density of states of graphene, and the Dirac point is in the band gap of the semiconductor substrate and coincides in energy with the local level of the separated (individual) carbon adatom. Graphene formed on a metal substrate also exhibits a zero-gap density of states. The problem of the band gap induced in graphene by a semiconductor substrate is considered in the general case. It is shown that, depending on the relation between the parameters of the problem, either one or two band gaps overlapping in energy with the band gap of the substrate can exist in the spectrum of graphene. The dependence of the band gaps on the strength of the graphene-substrate interaction is constructed. Numerical estimations are performed for epitaxial graphene formed on 6H-SiC$\{0001\}$ faces.