Electron-electron scattering and the electrical resistivity of metals

In this paper, we present the solution of the coupled Boltzmann equations which describe electrical transport in an interacting two-carrier system. In the isotropic case, these equations reduce to simple kinetic equations which allow a physical interpretation of the mechanisms governing the temperature dependence of the resistivity. Both electron-hole and $s-d$ scattering are considered. At low temperature, with a frequency-independent interaction, electron-electron scattering contributes a characteristic $T^2$ term to the resistivity, as in one-component systems. In the case of electron-hole scattering, the $T^2$ term can persist at high temperatures under certain conditions. The viriational principle is used to treat the effects of an anisotropic Fermi surface or scattering rate.