A new field-theoretical formulation for the motion of an electron in a quenched disorder potential

TL;DR

This paper introduces a novel field-theoretical approach to model the motion of electrons in disordered systems, utilizing functional integrals and auxiliary fields to simplify averaging over disorder.

Contribution

It develops a new formulation expressing Green functions as functional integrals with auxiliary fields, simplifying disorder averaging in noninteracting disordered Fermi systems.

Findings

Green functions expressed as functional integrals on a real time/frequency lattice

Normalization of the functional integral is unity due to specific identities

Method facilitates averaging over random disorder potential

Abstract

Following a proposal by Aronov and Ioselevich, we express the Green functions (GF) of a noninteracting disordered Fermi system as a functional integral on a real time/frequency lattice. The normalizing denominator of this functional integral is equal to unity, because of identities satisfied by the GF. The GF can then be simply averaged with respect to the random disorder potential. We describe the fermionic fields not belonging to the external frequency by means of a bosonic auxiliary field g. The Hubbard-Stratonovich field Q is introduced only with respect to the fermionic fields for the external frequency.