Lorenz ratio of an impure compensated metal in the degenerate Fermi liquid regime

Abstract

The Lorenz ratio serves as a measure to compare thermal and electric conductivities of metals. Recent experiments observed small Lorenz ratios in the compensated metal WP${}_2$, indicating that charge flow is strongly favored over heat conduction. Motivated by these findings, we study transport properties of compensated metals in the presence of electron-electron collisions and electron-impurity scattering. We focus on intermediate temperatures, where the phonon contributions to transport are weak and elastic and inelastic scattering rates are comparable. Our exact solution for the kinetic equation in the presence of general Fermi-liquid interactions is used to extract the Lorenz ratio for short and long range interactions. We find that the Lorenz ratio develops a temperature dependence and gets enhanced as a consequence of disorder scattering. For collisions mediated by the Coulomb interaction, impurities give rise to a non-monotonic dependence of the Lorenz ratio on the screening wave number with a minimum for intermediate screening strength. To help future experimental efforts, we establish a scheme to connect the exact results with the solution of the Boltzmann equation under the relaxation time approximation for all collision integrals. Our recipe provides simple phenomenological expressions for the transport coefficients and it allows for a physically transparent interpretation of the results.

21 pages, 9 figures, close to published version

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• Nonvanishing Energy Scales at the Quantum Critical Point of CeCoIn5
• Fermi surface of the Weyl type-II metallic candidate WP2
• Electronic thermal conductivity of disordered metals
• Thermal conductivity in the vicinity of the quantum critical endpoint in Sr3Ru2O7
• Thermal transport in compensated semimetals: a mystery explained
• The role of electron-electron collisions for charge and heat transport at intermediate temperatures

Cited by in corpus (1)

• Thermoelectric properties in semimetals with inelastic electron-hole scattering