Spin Hall Effect and Spin Transfer in Disordered Rashba Model

TL;DR

This paper numerically investigates the spin Hall effect in a disordered Rashba model, finding that disorder suppresses the effect beyond a certain length scale and prevents spin transfer, contrasting with quantum Hall behavior.

Contribution

It provides a numerical analysis showing the suppression of the topological spin Hall effect due to disorder in the Rashba model, highlighting differences from quantum Hall systems.

Findings

Spin Hall conductance remains finite up to a characteristic length scale.

All energy levels do not cross during flux insertion, indicating zero spin transfer.

Disorder causes the topological spin Hall effect to vanish.

Abstract

Based on numerical study of the Rashba model, we show that the spin Hall conductance remains finite in the presence of disorder up to a characteristic length scale, beyond which it vanishes exponentially with the system size. We further perform a Laughlin's gauge experiment numerically and find that all energy levels cannot cross each other during an adiabatic insertion of the flux in accordance with the general level-repulsion rule. It results in zero spin transfer between two edges of the sample as each state always evolves back after the insertion of one flux quantum, in contrast to the quantum Hall effect. It implies that the topological spin Hall effect vanishes with the turn-on of disorder.