A Criterion for Strange Metallicity in the Lorenz Ratio

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 $L_0={\pi }^2{k}_B^2/(3e^2)$ 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.

6 + 10 pages, published version includes a generalization of the criterion to the transverse Lorenz ratio

References in corpus (13)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Planckian Dissipation in Metals
• Universal theory of strange metals from spatially random interactions
• Large $N$ theory of critical Fermi surfaces II: conductivity
• Transport Properties of a spinon Fermi surface coupled to a U(1) gauge field
• Loop current fluctuations and quantum critical transport
• Thermal conductivity of a two-dimensional electron gas with Coulomb interaction
• Deviation from the Fermi-Liquid Transport Behavior in the Vicinity of a Van Hove Singularity
• The Wiedemann-Franz law in doped Mott insulators without quasiparticles
• Quantum Interference of Hydrodynamic Modes in a Dirty Marginal Fermi Liquid
• Breakdown of the Wiedemann-Franz law at the Lifshitz point of strained Sr${}_2$RuO${}_4$
• Thermal conductivity and heat diffusion in the two-dimensional Hubbard model

Cited by in corpus (7)

• Tunable non-Fermi liquid phase from coupling to two-level systems
• The Wiedemann-Franz law in doped Mott insulators without quasiparticles
• Solvable models of two-level systems coupled to itinerant electrons: Robust non-Fermi liquid and quantum critical pairing
• The Lorenz ratio as a guide to scattering contributions to Planckian transport
• Extended strange metal regime from superconducting puddles
• Fermi Surface Bosonization for Non-Fermi Liquids
• Lorenz ratios of diagonal and Hall conductivities in a Dirac electron liquid