High-temperature transport properties of a two-dimensional weakly doped parabolic semiconductor

A version of the Mexican-hat Hamiltonian is used to study high-temperature transport properties of a two-dimensional weakly doped semiconductor with electron-hole symmetric bands. For a finite doping level and a temperature-dependent band gap, we find a closed analytical form of the temperature-dependent chemical potential. The effective concentrations of charge carriers participating in transport coefficients are analyzed in the space spanned by the total electron concentration and temperature. It is shown that these concentrations are the sum of a residual contribution and two thermally activated contributions, with a complicated dependence on temperature. The analytical expression for the Hall coefficient RHis also found. It is argued that it is a non-monotonic function of the doping level with the maximum at the doping nmax that is a linear function of temperature at high enough temperatures. The analysis of the real part of the interband conductivity shows that it is inversely proportional to incoming photon energy at low temperatures and that it is nearly constant over a wide energy range at high temperatures. This results are expected to be of significant importance in understanding transport and optical properties of weakly doped two-dimensional semiconductors with nearly symmetric parabolic bands. .