Electron-electron Relaxation in Disordered Interacting Systems

TL;DR

This paper investigates how electron-electron interactions and disorder influence the relaxation dynamics of non-equilibrium carriers, revealing exponential relaxation behavior and the impact of disorder on relaxation rates.

Contribution

It introduces a microscopic approach using the equation-of-motion for the density matrix to study relaxation in disordered interacting systems based on the Anderson model.

Findings

Relaxation is exponential during initial dynamics.

Relaxation rate decreases with increasing disorder.

Total energy remains conserved during redistribution.

Abstract

We study the relaxation of a non-equilibrium carrier distribution under the influence of the electron-electron interaction in the presence of disorder. Based on the Anderson model, our Hamiltonian is composed from a single particle part including the disorder and a two-particle part accounting for the Coulomb interaction. We apply the equation-of-motion approach for the density matrix, which provides a fully microscopic description of the relaxation. Our results show that the nonequlibrium distribution in this closed and internally interacting system relaxes exponentially fast during the initial dynamics. This fast relaxation can be described by a phenomenological damping rate. The total single particle energy decreases in the redistribution process, keeping the total energy of the system fixed. It turns out that the relaxation rate decreases with increasing disorder.