Variable range hopping in the Coulomb gap and gate screening in two dimensions

We simulate the single particle ground state and variable range hopping (VRH) in the two-dimensional model of doped semiconductors. The obtained results show a universality of the linear Coulomb gap in the density of states at the Fermi energy as well as the Efros-Shklovskii (ES) T−1/2-law for the temperature dependence of VRH resistivity. The screening due to the metallic gate smears the Coulomb gap, and therefore, may produce the crossover from ES to Mott VRH as the temperature decreases. The full range of temperature of such a crossover seems however to be very large, up to three orders of magnitude.