Interaction corrections: temperature and parallel field dependencies of the Lorentz number in two-dimensional disordered metals

TL;DR

This paper investigates how electron-electron interactions affect thermal and electrical transport in two-dimensional disordered metals under parallel magnetic fields, revealing deviations from the Wiedemann-Franz law across different regimes.

Contribution

It provides a detailed theoretical analysis of the temperature and magnetic field dependence of the Lorentz number in disordered metals, including the identification of regimes and interaction effects.

Findings

Electron-electron interactions cause deviations from the Wiedemann-Franz law.

The Lorentz number's dependence on temperature and magnetic field varies across regimes.

Non-monotonic behavior of the Lorentz number is observed with applied magnetic field.

Abstract

The electron-electron interaction corrections to the transport coefficients are calculated for a two-dimensional disordered metal in a parallel magnetic field via the quantum kinetic equation approach. For the thermal transport, three regimes (diffusive, quasiballistic and truly ballistic) can be identified as the temperature increases. For the diffusive and quasiballistic regimes, the Lorentz number dependence on the temperature and on the magnetic field is studied. The electron-electron interactions induce deviations from the Wiedemann-Franz law, whose sign depend on the temperature: at low temperatures the long-range part of the Coulomb interaction gives a positive correction, while at higher temperature the inelastic collisions dominate the negative correction. By applying a parallel field, the Lorentz number becomes a non-monotonic function of field and temperature for all values of the Fermi-liquid interaction parameter in the diffusive regime, while in the quasiballistic case this is true only sufficiently far from the Stoner instability.