Two Interacting Electrons in a Disorder Potential: Localization Properties

TL;DR

This paper provides an analytical solution for two interacting electrons in a disordered quasi-one-dimensional wire, revealing how their interaction influences the density of states and localization length, with a criterion for when these effects occur.

Contribution

It offers a complete analytical solution to the two-electron problem in a disordered wire using supersymmetry, highlighting the impact of interactions on localization properties.

Findings

Interaction modifies the density of states.

Localization length is affected by two-body interactions.

A criterion for the onset of localization length change is derived.

Abstract

Two electrons move in a quasi one--dimensional wire under the influence of a short--range interaction. We restrict Hilbert space to those states where the two electrons are close to each other. Using supersymmetry, we present a complete analytical solution to this problem. The two--body interaction affects the density of states and, thereby, the localization length. We derive a criterion for the onset of changes of the localization length due to the two--body interaction.