A Criterion for Strange Metallicity in the Lorenz Ratio

TL;DR

This paper proposes using the low-temperature correction to the Lorenz ratio as a criterion to distinguish strange metals from Fermi liquids, revealing different temperature dependencies in their inelastic scattering rates.

Contribution

It introduces a new diagnostic based on the low-temperature correction to the Lorenz ratio to identify strange metallic behavior, supported by solvable models and quantum Boltzmann equation analysis.

Findings

In a marginal Fermi liquid, $L(T)-L_0 o -T$ at low temperatures.

In Fermi liquids, $L(T)-L_0 o -T^2$, even with linear resistivity.

The transverse Lorenz ratio exhibits the same temperature dependence as the longitudinal one.

Abstract

The Wiedemann-Franz (WF) law, stating that the Lorenz ratio $L = \kappa/(T\sigma)$ 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 $T \to 0$. 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, $L(T)-L_0\propto -T$. 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, $L_{xy} = \kappa_{xy}/(T\sigma_{xy})$, exhibits the same behavior.