Quantized spin Hall effect in Helium three-A and other p-wave paired Fermi systems

TL;DR

This paper predicts a quantized spin Hall effect in 3D p-wave superfluid systems like Helium-3 A-phase, extending known 2D effects to three dimensions and suggesting experimental observation in cold Fermi gases.

Contribution

It introduces the concept of a quantized spin Hall effect in 3D p-wave paired Fermi systems, generalizing previous 2D and charge Hall effects to spin transport.

Findings

Proposes the SHE in Helium-3 A-phase and similar systems.

Extends the SHE concept from 2D to 3D systems.

Suggests experimental conditions for observing SHE in cold Fermi gases.

Abstract

In this paper we propose the quantized spin Hall effect (SHE) in the vortex state of a rotating p-wave paired Fermi system in an inhomogeneous magnetic field and in a weak periodic potential. It is the three dimensional extension of the spin Hall effect for a 3He-A superfluid film studied in Ref. [1]. It may also be considered as a generalization of the 3D quantized charge Hall effect of Bloch electrons in Ref. [2] to the spin transport. The A-phase of 3He or, more generally, the p-wave paired phase of a cold Fermi atomic gas, under suitable conditions should be a good candidate to observe the SHE, because the system has a conserved spin current (with no spin-orbit couplings).