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 $\sigma$ of epitaxial graphene has been calculated according to the Kubo–Greenwood formula. The quantity $\sigma_m$ of undoped graphene on metal has been shown to decrease with an increase in the deviation of the Dirac point $\varepsilon_{\mathrm{D}}$ (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 $\sigma_{\mathrm{sc}}$ turns out to be nonzero and amounts to $\sigma_{\mathrm{sc}} = 2e^2/\pi\hbar$-only under the condition $\varepsilon_{\mathrm{F}}=\varepsilon'_{\mathrm{D}}$, where $\varepsilon'_{\mathrm{D}}$, is the Dirac-point energy renormalized by the interaction with the substrate.
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