▎ 摘　　要

The transport properties of epitaxial graphene formed on the surface of a semiconductor substrate are considered. An approach based on the model Anderson Hamiltonian in the Haldane-Anderson approximation is used. An analytical expression for the density of states of epitaxial graphene is derived. The behavior of the density of states of epitaxial graphene is studied for various problem parameters. The real part of the dynamic conductivity of epitaxial graphene is studied; the limit conductivity and its dependences on the chemical potential and temperature are considered. It is shown that the conductivity of epitaxial graphene abruptly changes near the semiconductor-gap edges. When graphene-substrate interaction is zero, the static conductivity of epitaxial graphene takes a universal value of 2e (2)/pi. The thermoelectric power of epitaxial graphene is studied; it is shown that this parameter anomalously increases near the semiconductor-gap edges. By analogy with the electronic topological transition in metals, this effect can be attributed to the formation of a new class of quasiparticles with a lifetime strongly dependent on energy (a new scattering channel). The considered fundamental problems are of critical importance in studying the optical, magneto-optical, thermoelectric, and thermomagnetic properties of epitaxial graphene. The results obtained are of particular interest when considering epitaxial graphene as a promising material for ultrahigh-frequency engineering.