The role of electron-electron collisions for charge and heat transport at intermediate temperatures

We study electric, thermal and thermoelectric transport in correlated electron systems in the intermediate temperature regime, in which elastic and inelastic scattering are both important. To this end, we study the Boltzmann equation in the presence of an electric field and a temperature gradient for two cases: First, when electron-electron collisions are treated within the relaxation-time approximation while the full momentum dependence of electron-impurity scattering is included and, second, when the electron-impurity scattering is momentum-independent, but the electron-electron collisions give rise to a momentum-dependent inelastic scattering rate of the Fermi-liquid type. We find that the inelastic relaxation rate enters the electric conductivity and the Seebeck coefficient only when the momentum dependence of the electron-impurity collisions is included. Specifically, we show that inelastic processes only mildly affect the electric conductivity, but can generate a non-monotonic dependence of the Seebeck coefficient on temperature and even a change of sign. Thermal conductivity always depends on the inelastic scattering rate even for a constant elastic relaxation rate.