The Lorenz ratio of an impure compensated metal at intermediate temperatures

Recent experiments observed small Lorenz ratios in the compensated metal WP2, indicating that charge flow is strongly favored over heat conduction. Motivated by these findings, we study transport properties of compensated metals in the presence of electron-electron collisions and electron-impurity scattering. We focus on intermediate temperatures, where the phonon contributions to transport are weak and elastic and inelastic scattering rates are comparable. Our exact solution for the kinetic equation in the presence of general Fermi-liquid interactions is used to extract the Lorenz ratio for short and long range interactions. We find that the Lorenz ratio develops a temperature dependence as well as gets enhanced as a consequence of disorder scattering. For collisions mediated by the Coulomb interaction, impurities give rise to a non-monotonic dependence of the Lorenz ratio on the screening wave number. To help future experimental efforts, we establish a scheme to connect the exact results with the solution of the Boltzmann equation under the relaxation time approximation for all collision integrals, providing simple phenomenological expressions for the transport coefficients.