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.

arXiv comment6 + 10 pages, published version includes a generalization of the criterion to the transverse Lorenz ratio

References in corpus (45)

• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Fermi-liquid instabilities at magnetic quantum phase transitions
• Strange metal in magic-angle graphene with near Planckian dissipation
• Resistivity as a function of temperature for models with hot spots on the Fermi surface.
• Universal $T$-linear resistivity and Planckian limit in overdoped cuprates
• Interplay of disorder and spin fluctuations in the resistivity near a quantum critical point
• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Heat Transport in a Strongly Overdoped Cuprate: Fermi Liquid and Pure d-wave BCS Superconductor
• Phonon-induced giant linear-in-$T$ resistivity in magic angle twisted bilayer graphene: Ordinary strangeness and exotic superconductivity
• Charged impurity scattering limited low temperature resistivity of low density silicon inversion layers
• Linear in Temperature Resistivity and Associated Mysteries
• Planckian Dissipation in Metals
• Phonons become chiral in the pseudogap phase of cuprates
• Non-Fermi liquids and the Wiedemann-Franz law
• Universal theory of strange metals from spatially random interactions
• Linear-in temperature resistivity from an isotropic Planckian scattering rate
• Wiedemann-Franz law and Fermi liquids
• Violation of the Wiedemann-Franz law in clean graphene layers
• Quantum critical response at the onset of spin density wave order in two-dimensional metals
• Large $N$ theory of critical Fermi surfaces II: conductivity
• Transport Properties of a spinon Fermi surface coupled to a U(1) gauge field
• Electronic hydrodynamics and the breakdown of the Wiedemann-Franz and Mott laws in interacting metals
• Heat Transport as a Probe of Electron Scattering by Spin Fluctuations: the Case of Antiferromagnetic CeRhIn5
• Transport coefficients of graphene: Interplay of impurity scattering, Coulomb interaction, and optical phonons
• Theory of the Strange Metal Sr${}_3$Ru${}_2$O${}_7$
• Loop current fluctuations and quantum critical transport
• Wiedemann-Franz law in the underdoped cuprate superconductor YBa2Cu3Oy
• Quantum kinetic approach for studying thermal transport in the presence of electron-electron interactions and disorder
• Screening and transport in 2D semiconductor systems at low temperatures
• Low temperature $T$-linear resistivity due to umklapp scattering from a critical mode
• Thermal conductivity of a two-dimensional electron gas with Coulomb interaction
• Electron-electron interaction corrections to the thermal conductivity in disordered conductors
• Deviation from the Fermi-Liquid Transport Behavior in the Vicinity of a Van Hove Singularity
• Wiedemann-Franz law and non-vanishing temperature scale across the field-tuned quantum critical point of YbRh2Si2
• Transport and Thermodynamic Evidence for a Marginal Fermi Liquid State in ZrZn${}_2$
• The Wiedemann-Franz law in doped Mott insulators without quasiparticles
• Thermal Transport and Wiedemann-Franz Law in the Disordered Fermi Liquid
• Quantum Interference of Hydrodynamic Modes in a Dirty Marginal Fermi Liquid
• Transport Anomalies and Marginal Fermi-Liquid Effects at a Quantum Critical Point
• Know the enemy: 2D Fermi liquids
• Breakdown of the Wiedemann-Franz law at the Lifshitz point of strained Sr${}_2$RuO${}_4$
• Conductivity close to antiferromagnetic criticality
• Thermal conductivity and heat diffusion in the two-dimensional Hubbard model
• Theory of Thermal Conductivity in the Disordered Electron Liquid

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• Tunable non-Fermi liquid phase from coupling to two-level systems
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• 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