Lorentz ratio of a compensated metal

TL;DR

This paper derives the Lorentz ratio for a clean compensated metal with dominant intercarrier scattering, revealing conditions for violation of the Wiedemann-Franz law, and applies the model to explain experimental observations in WP2.

Contribution

It provides an exact solution for the Lorentz ratio in a compensated metal with intercarrier interactions, highlighting the forward-scattering limit and explaining experimental violations in WP2.

Findings

Lorentz ratio can be arbitrarily small in the forward-scattering limit.

Exact solution for the Lorentz ratio in a compensated metal.

Application to explain violations in WP2.

Abstract

A violation of the Wiedemann-Franz law in a metal can be quantified by comparing the Lorentz ratio, $L=\kappa\rho/T$, where $\kappa$ is the thermal conductivity and $\rho$ is the electrical resistivity, with the universal Sommerfeld constant, $L_0=(\pi^2/3) (k_B/e)^2$. We obtain the Lorentz ratio of a clean compensated metal with intercarrier interaction as the dominant scattering mechanism by solving exactly the system of coupled integral Boltzmann equations. The Lorentz ratio is shown to assume a particular simple form in the forward-scattering limit: $L/L_0=\overline{\Theta^2}/2$, where $\Theta$ is the scattering angle. In this limit, $L/L_0$ can be arbitrarily small. We also show how the same result can be obtained without the benefit of an exact solution. We discuss how a strong downward violation of the Wiedemann-Franz law in a type-II Weyl semimetal WP$_2$ can be explained within our model.