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 ${}^3\text{H}\text{e}$-A superfluid film previously studied in the literature. It may also be considered as a generalization of the three-dimensional quantized charge Hall effect of Bloch electrons in the work previously studied in the literature to the spin transport. The A phase of ${}^3\text{H}\text{e}$ 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).

• Received 7 December 2006

DOI:https://doi.org/10.1103/PhysRevB.77.144504