Theory of Thermal Conductivity in the Disordered Electron Liquid

TL;DR

This paper analyzes how long-range Coulomb interactions affect thermal conductivity in disordered two-dimensional electron liquids, revealing a logarithmic correction that violates the Wiedemann-Franz law and remains unaffected by Fermi liquid interactions.

Contribution

It extends the RG analysis for thermal transport to include Coulomb scattering processes, providing a final correction estimate applicable near the metal-insulator transition.

Findings

Logarithmic correction to thermal conductivity due to Coulomb interactions.

Violation of the Wiedemann-Franz law in the disordered electron liquid.

Sub-temperature correction remains unchanged by Fermi liquid interactions.

Abstract

We study thermal conductivity in the disordered two-dimensional electron liquid in the presence of long-range Coulomb interactions. We describe a microscopic analysis of the problem using as a starting point the partition function defined on the Keldysh contour. We extend the Renormalization Group (RG) analysis developed for thermal transport in the disordered Fermi liquid, and include scattering processes induced by the long-range Coulomb interaction in the sub-temperature energy range. For the thermal conductivity, unlike for the electric conductivity, these scattering processes yield a logarithmic correction which may compete with the RG-corrections. The interest in this correction arises from the fact that it violates the Wiedemann-Franz law. We checked that the sub-temperature correction to the thermal conductivity is not modified, neither by the inclusion of Fermi liquid interaction amplitudes nor as a result of the RG flow. We thereby expect that the answer obtained for this correction is final. We use the theory to describe thermal transport on the metallic side of the metal-insulator transition in Si MOSFETs.