Transport in two-dimensional quantum wires with point scatterers. The Wigner-Smith time delay

TL;DR

This paper investigates electronic transport in disordered 2D quantum wires with point scatterers, analyzing conductance, S-matrix statistics, and Wigner-Smith time delay, especially in localization regimes, comparing results with 1D models.

Contribution

It provides a detailed analysis of transport regimes in 2D quantum wires with point impurities, including the distribution of Wigner-Smith time delay in localization.

Findings

Wigner-Smith time delay distribution matches 1D random potential predictions in localization regime

Conductance and S-matrix statistics are characterized for intermediate and localized regimes

Disorder modeled via uniformly distributed point scatterers in a 2D quantum wire

Abstract

Electronic transport properties of the disordered quantum wires are considered. The disorder is introduced via impurities (point scatterers), distributed uniformly over the two-dimensional strip, which represents a model quantum wire. Incident electrons with a given energy are scattered on impurities and boundaries of the wire. The electron-electron interaction is neglected in the model. In particular, the intermediate regime and the localization regime of transport are studied in more detail in terms of the conductance and statistical properties of S-matrix ensemble for a given incident electron energy. The Wigner-Smith time delay distribution obtained for the localization regime is compared with the prediction for the scattering by a one-dimensional random potential.