Mesoscopic Spin Hall Effect

TL;DR

This paper studies the mesoscopic spin Hall effect in ballistic chaotic quantum dots with spin-orbit coupling, showing how a charge current can generate a transverse spin current with universal fluctuations.

Contribution

It provides analytical and numerical analysis of the spin Hall effect in quantum dots, highlighting the conditions for universal fluctuations of the transverse spin current.

Findings

Transverse spin current fluctuates universally with zero average for large spin-orbit coupling times.

Finite typical transverse spin current proportional to bias V, about one excess open channel.

Analytical results agree with numerical simulations in diffusive and chaotic systems.

Abstract

We investigate the spin Hall effect in ballistic chaotic quantum dots with spin-orbit coupling. We show that a longitudinal charge current can generate a pure transverse spin current. While this transverse spin current is generically nonzero for a fixed sample, we show that when the spin-orbit coupling time is large compared to the mean dwell time inside the dot, it fluctuates universally from sample to sample or upon variation of the chemical potential with a vanishing average. For a fixed sample configuration, the transverse spin current has a finite typical value ~e^2 V/h, proportional to the longitudinal bias V on the sample, and corresponding to about one excess open channel for one of the two spin species. Our analytical results are in agreement with numerical results in a diffusive system [W. Ren et al., Phys. Rev. Lett. 97, 066603 (2006)] and are further confirmed by numerical simulation in a chaotic cavity.