Lorentz ratio of a compensated metal

Abstract

A violation of the Wiedemann-Franz law in a metal can be quantified by comparing the Lorentz ratio, $L=\kappa \rho /T$, where $\kappa$ is the thermal conductivity and $\rho$ is the electrical resistivity, with the universal Sommerfeld constant, $L_0=({\pi }^2/3)(k_B/e{)}^2$. We obtain the Lorentz ratio of a clean compensated metal with intercarrier interaction as the dominant scattering mechanism by solving exactly the system of coupled integral Boltzmann equations. The Lorentz ratio is shown to assume a particular simple form in the forward-scattering limit: $L/L_0=\overline{{\Theta }^2}/2$, where $\Theta$ is the scattering angle. In this limit, $L/L_0$ can be arbitrarily small. We also show how the same result can be obtained without the benefit of an exact solution. We discuss how a strong downward violation of the Wiedemann-Franz law in a type-II Weyl semimetal WP${}_2$ can be explained within our model.

published version, 15 pages, 2 figures

References in corpus (10)

• Slow imbalance relaxation and thermoelectric transport in graphene
• Quantum-critical relativistic magnetotransport in graphene
• Departure from the Wiedemann-Franz Law in WP${}_2$ Driven by Mismatch in $T$-square Resistivity Prefactors
• Microscopic Origins of Hydrodynamic Transport in Type-II Weyl Semimetal WP${}_2$
• Anomalous reduction of the Lorenz ratio at the quantum critical point in YbAgGe
• Magnetoresistance of semi-metals: the case of antimony
• Stable Weyl points, trivial surface states and particle-hole compensation in WP2
• Thermal conductivity of a two-dimensional electron gas with Coulomb interaction
• Thermal conductivity in the vicinity of the quantum critical endpoint in Sr3Ru2O7
• Cooper channel and the singularities in the thermodynamics of a Fermi liquid

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