A criterion for strange metallicity in the Lorenz ratio

The Wiedemann-Franz (WF) law, stating that the Lorenz ratio L = κ/(T σ) between the thermal and electrical conductivities in a metal approaches a universal constant L0=π2kB2/(3e2) 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) − L ₀ (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) − L ₀ ∝ − 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) − L ₀ is proportional to − T ². 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, L_{x y} = κ_{x y}/(T σ_{x y}), exhibits the same behavior.