Lorentz ratio of a compensated metal

A violation of the Wiedemann-Franz law in a metal can be quantified by comparing the Lorentz ratio, $L=κρ/T$, where $κ$ is the thermal conductivity and $ρ$ is the electrical resistivity, with the universal Sommerfeld constant, $L_0=(π^2/3) (k_B/e)^2$. 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: $L/L_0=\overline{Θ^2}/2$, where $Θ$ 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.