Quantum kinetic theory: The disordered electron problem

TL;DR

This paper introduces quantum kinetic theory for noninteracting electrons in disordered solids, deriving the quantum Boltzmann equation, analyzing conductivity, and discussing interference effects and electron-electron interactions.

Contribution

It provides a comprehensive derivation of the quantum Boltzmann equation and analyzes disorder effects, including weak localization, in disordered electronic systems.

Findings

Derivation of quantum Boltzmann equation for disordered electrons

Analysis of electrical conductivity and density response

Discussion of wave interference and electron-electron interactions

Abstract

These are notes for lectures delivered at the NATO ASI on Dynamics in Leiden, The Netherlands, in July 1998. The quantum kinetic theory for noninteracting electrons in a disordered solid is introduced and discussed. We first use many-body theory to derive the quantum Boltzmann equation that describes transport and time correlation functions in this system. Particular attention is paid to the calculation of the electrical conductivity and the density response function. We then consider corrections to the Boltzmann equation due to wave interference effects. The disorder expansion of the conductivity is addressed, and the so-called weak localization or long-time tail contribution to the conductivity is discussed. We conclude with a brief discussion of the influence of electron-electron interactions on the properties of disordered electronic systems.