Scattering and transport statistics at criticality

TL;DR

This study numerically investigates the scattering and transport properties of the 1D Anderson model at criticality using the PBRM model, revealing a transition from localized to delocalized behavior and comparing results with 3D Anderson models.

Contribution

It provides a detailed numerical analysis of scattering and transport at the metal-insulator transition using the PBRM model, highlighting its agreement with 3D Anderson model properties.

Findings

Smooth transition in scattering matrix elements with bandwidth variation

Conductance distribution and shot noise power change from localized to delocalized regimes

PBRM model with specific parameters reproduces 3D Anderson critical behavior

Abstract

We study numerically scattering and transport statistical properties of the one-dimensional Anderson model at the metal-insulator transition described by the Power-law Banded Random Matrix (PBRM) model at criticality. Within a scattering approach to electronic transport, we concentrate on the case of a small number of single-channel attached leads. We observe a smooth transition from localized to delocalized behavior in the average scattering matrix elements, the conductance probability distribution, the variance of the conductance, and the shot noise power by varying $b$ (the effective bandwidth of the PBRM model) from small ($b\ll 1$) to large ($b>1$) values. We contrast our results with analytic random matrix theory predictions which are expected to be recovered in the limit $b\to \infty$. We also compare our results for the PBRM model with those for the three-dimensional (3D) Anderson model at criticality, finding that the PBRM model with $b \in [0.2,0.4]$ reproduces well the scattering and transport properties of the 3D Anderson model.