Omnidirectional spin Hall effect in a Weyl spin-orbit coupled atomic gas

The three-dimensional (3D) Weyl spin-orbit coupling (SOC) can be created for ultracold atoms by laser coupling four atomic internal states [1] or using a specially chosen sequence of inhomogeneous magnetic pulses [2]. It is now shown that applying such a 3D Weyl SOC, a transverse spin current is generated in response to either a constant spin-independent force or a time-dependent Zeeman field in an arbitrary direction [3]. This effect is the non-Abelian counterpart of the universal intrinsic spin Hall effect characteristic of the two-dimensional Rashba SOC. We quantify the strength of such an omnidirectional spin Hall effect by calculating the corresponding conductivity for fermions and non-condensed bosons. The absence of any kind of disorder in ultracold-atom systems makes the observation of this effect viable.
[1] B. M. Anderson, G. Juzeliunas, V. M. Galitski, and I. B. Spielman, Synthetic 3D Spin-Orbit Coupling, Phys. Rev. Lett. 108, 235301 (2012)
[2] B. M. Anderson, I. B. Spielman, and G. Juzeliunas, Magnetically Generated Spin-Orbit Coupling for Ultracold Atoms, Phys. Rev. Lett. 111, 125301 (2013).
[3] J. Armaitis, J. Ruseckas, and G. Juzeliunas, Omnidirectional spin Hall effect in a Weyl spin-orbit-coupled atomic gas, Phys. Rev. A 95, 033635 (2017).