Friedel oscillations in disordered quantum wires: Influence of e-e interactions on the localization length

TL;DR

This paper numerically investigates Friedel oscillations in disordered interacting quantum wires, demonstrating how disorder and electron-electron interactions influence the localization length, which is linked to the exponential decay of oscillations.

Contribution

It introduces a numerical method to connect Friedel oscillation decay with the Anderson localization length in disordered quantum wires with interactions.

Findings

Friedel oscillations decay exponentially in disordered systems.

Localization length decreases with increasing electron-electron interaction strength.

Scaling of oscillations reveals the dependence of localization length on disorder and interactions.

Abstract

The Friedel oscillations caused due to an impurity located at one edge of a disordered interacting quantum wire are calculated numerically. The electron density in the system's ground state is determined using the DMRG method, and the Friedel oscillations data is extracted using the density difference between the case in which the wire is coupled to an impurity and the case where the impurity is uncoupled. We show that the power law decay of the oscillations occurring for an interacting clean 1D samples described by Luttinger liquid theory, is multiplied by an exponential decay term due to the disorder. Scaling of the average Friedel oscillations by this exponential term collapses the disordered samples data on the clean results. We show that the length scale governing the exponential decay may be associated with the Anderson localization length and thus be used as a convenient way to determine the dependence of the localization length on disorder and interactions. The localization length decreases as a function of the interaction strength, in accordance with previous predictions.