Lorenz ratio of an impure compensated metal in the degenerate Fermi liquid regime

TL;DR

This paper investigates how impurity scattering and electron-electron interactions influence the Lorenz ratio in compensated metals, revealing temperature-dependent behavior and non-monotonic effects relevant for experimental observations.

Contribution

The study provides an exact solution for the Lorenz ratio in compensated metals considering general Fermi-liquid interactions and introduces a practical scheme to connect these results with Boltzmann equation approaches.

Findings

Lorenz ratio depends on temperature and disorder scattering.

Impurities cause a non-monotonic Lorenz ratio dependence on screening strength.

The paper offers phenomenological expressions for transport coefficients.

Abstract

The Lorenz ratio serves as a measure to compare thermal and electric conductivities of metals. Recent experiments observed small Lorenz ratios in the compensated metal WP$_2$, 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 and 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 with a minimum for intermediate screening strength. 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. Our recipe provides simple phenomenological expressions for the transport coefficients and it allows for a physically transparent interpretation of the results.