Electron--electron scattering and conductivity of disordered systems with Galilean-invariant spectrum

TL;DR

This paper investigates how electron-electron interactions influence electrical resistivity in disordered systems with Galilean-invariant spectra, revealing that such interactions can affect resistivity through Fermi surface redistribution when combined with impurity scattering.

Contribution

It demonstrates that electron-electron collisions can impact resistivity in systems with multiply connected Fermi surfaces, even when they do not directly affect current.

Findings

Electron-electron collisions cause Fermi surface redistribution.

Resistivity is affected by electron-electron interactions in the presence of impurity scattering.

The effect is significant in systems with multiple filled subbands.

Abstract

The electron--electron scattering does not affect the electrical current in Galilean--invariant systems. We show that nevertheless electron--electron collisions may contribute to the electric resistivity of systems with parabolic spectrum provided that they have multiply connected Fermi surface and there is an additional mechanism of scattering. To this end, we calculate the resistivity of a two-dimensional electron gas with two filled transverse subbands in a presence of electron--electron and impurity scattering. Though the collisions between the electrons do not directly affect the current in such systems, they cause a redistribution of the electrons between the Fermi contours, which results in a noticeable change of resistivity for realistic mechanisms of impurity scattering.