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

TL;DR

This paper develops a quantum kinetic equation approach to analyze electron-electron interaction corrections to thermal and electrical transport in disordered metals, revealing violations of the Wiedemann-Franz law due to neutral bosons.

Contribution

It introduces a local quantum kinetic framework with bosonic distribution functions to distinguish processes affecting charge and energy transport in disordered metals.

Findings

Wiedemann-Franz law is always violated by interaction corrections.

Violation is more pronounced in 1D and 2D diffusive regimes.

Neutral bosons significantly contribute to energy transport, causing the law's breakdown.

Abstract

We consider the singular electron-electron interaction corrections to the 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 obeyed. 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 the charge and energy transport: elastic electron scattering affects both, while the inelastic processes influence only the latter. Moreover, the neutral bosons, though incapable of transporting charge, contribute significantly to the energy transport. In our approach we calculate on equal footing the electrical and thermal conductivities and the specific heat in any dimension. We found 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 $T\tau \ll \hbar$ and it is due to the energy transported by the neutral bosons. For two-dimensional systems in the quasi-ballistic regime $T\tau \gg \hbar$ the inelastic scattering of the electron on the bosons also contributes to the violation.