Interaction corrections to thermal transport coefficients in disordered metals: The quantum kinetic equation approach

Abstract

We consider singular electron-electron interaction corrections to transport coefficients in disordered metals to test the validity of the Wiedemann-Franz law. We develop a local, quantum kinetic equation approach in which the charge and energy conservation laws are explicitly satisfied. To obtain the local description, we introduce bosonic distribution functions for the neutral low-energy collective modes (electron-hole pairs). The resulting system of kinetic equations enables us to distinguish between the different physical processes involved in charge and energy transport: elastic electron scattering affects both, while the inelastic processes influence only the latter. Moreover, neutral bosons, although incapable of transporting charge, contribute significantly to energy transport. In our approach, we calculate on equal footing the electric and thermal conductivities and the specific heat in each dimension. We find that the Wiedemann-Franz law is always violated by the interaction corrections; the violation is larger for one-and two-dimensional systems in the diffusive regime Tτ≪ and is due to the energy transported by neutral bosons. For two-dimensional systems in the quasi-ballistic regime Tτ≫, the inelastic scattering of the electron on the bosons also contributes to the violation.