Localization Properties of Two Interacting Electrons in a Disordered Quasi One-Dimensional Potential

TL;DR

This paper investigates how short-range interactions between two electrons affect their localization length in a disordered quasi-one-dimensional wire, using supersymmetry and non-linear sigma models to derive a simple expression for the interaction-induced change.

Contribution

It introduces a novel analytical approach to quantify the impact of two-body interactions on electron localization in disordered systems.

Findings

Derived a simple expression for the change in localization length due to interactions.

Applied supersymmetry and non-linear sigma models to analyze two-electron transport.

Provided insights into the role of interactions in disordered quantum wires.

Abstract

We study the transport properties of two electrons in a quasi one-dimensional disordered wire. The electrons are subject to both, a disorder potential and a short range two-body interaction. Using the approach developed by Iida et al. [ Ann. Phys. (N.Y.) 200 (1990) 219 ], the supersymmetry technique, and a suitable truncation of Hilbert space, we work out the two-point correlation function in the framework of a non-linear sigma model. We study the loop corrections to arbitrary order. We obtain a remarkably simple and physically transparent expression for the change of the localization length caused by the two-body interaction.