Finite size effects and localization properties of disordered quantum wires with chiral symmetry

TL;DR

This paper investigates how finite size and disorder, introduced via vacancies, affect the localization and conductance of chiral symmetric quantum wires, revealing exponential decay, finite size effects, and a transition to ultra-localized states.

Contribution

It provides an analytical formula for mean conductance in disordered quantum wires with chiral symmetry, capturing finite size effects and localization transitions.

Findings

Mean conductance decays exponentially with wire length at low vacancy concentration.

Finite size effects cause non-exponential conductance decay in wide wires.

A critical vacancy concentration induces a transition to ultra-localized states.

Abstract

Finite size effects in the localization properties of disordered quantum wires are analyzed through conductance calculations. Disorder is induced by introducing vacancies at random positions in the wire and thus preserving the chiral symmetry. For quasi one-dimensional geometries and low concentration of vacancies, an exponential decay of the mean conductance with the wire length is obtained even at the center of the energy band. For wide wires, finite size effects cause the conductance to decay following a non-pure exponential law. We propose an analytical formula for the mean conductance that reproduces accurately the numerical data for both geometries. However, when the concentration of vacancies increases above a critical value, a transition towards the suppression of the conductance occurs. This is a signature of the presence of ultra-localized states trapped in finite regions of the sample.