A criterion for strange metallicity in the Lorenz ratio

Abstract

The Wiedemann-Franz (WF) law, stating that the Lorenz ratio L = κ/(Tσ) between the thermal and electrical conductivities in a metal approaches a universal constant {L}_{0}={pi }^{2}{k}_{B}^{2}/(3{e}^{2}) at low temperatures, is often interpreted as a signature of fermionic Landau quasi-particles. In contrast, we show that various models of weakly disordered non-Fermi liquids also obey the WF law at T → 0. Instead, we propose using the leading low-temperature correction to the WF law, L(T) − L0 (proportional to the inelastic scattering rate), to distinguish different types of strange metals. As an example, we demonstrate that in a solvable model of a marginal Fermi-liquid, L(T) − L0 ∝ − T. Using the quantum Boltzmann equation (QBE) approach, we find analogous behavior in a class of marginal- and non-Fermi liquids with a weakly momentum-dependent inelastic scattering. In contrast, in a Fermi-liquid, L(T) − L0 is proportional to − T2. This holds even when the resistivity grows linearly with T, due to T − linear quasi-elastic scattering (as in the case of electron-phonon scattering at temperatures above the Debye frequency). Finally, by exploiting the QBE approach, we demonstrate that the transverse Lorenz ratio, Lxy = κxy/(Tσxy), exhibits the same behavior.