On the fermi velocity and static conductivity of epitaxial graphene

Abstract

The models of the energy density of states of a metallic or semiconductor substrate, which does not further lead to divergences, have been proposed to calculate the characteristics of epitaxial graphene. The Fermi velocity of epitaxial graphene formed on a metal has been shown to be greater than that in free-standing graphene irrespective of the position of the Fermi level. On the contrary, the Fermi velocity of graphene formed on a semiconductor is lower so that the lower is the Fermi velocity, the closer is the Fermi level to the center of the band gap of the semiconductor. The zero-temperature static conductivity σ of epitaxial graphene has been calculated according to the Kubo-Greenwood formula. The quantity σm of undoped graphene on metal has been shown to decrease with an increase in the deviation of the Dirac point ɛD (which coincides with the Fermi level of the system) from the center of the conduction band of the substrate. In the case of the semiconductor substrate, the static conductivity σsc turns out to be nonzero and amounts to σsc = 2e2/πħ-only under the condition ɛF =ɛ′D, where ɛ′D is the Dirac-point energy renormalized by the interaction with the substrate.