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 =κ ρ /T , where κ is the thermal conductivity and ρ is the electrical resistivity, with the universal Sommerfeld constant, L₀=(π²/3 ) (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 /L₀=Θ²¯/2 , where Θ is the scattering angle. In this limit, L /L₀ 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 WP₂ can be explained within our model.