Inhomogeneous Rashba spin-orbit coupling and intrinsic spin-Hall effect

The spin-Hall effect is the generation of a transverse spin-current induced by a longitudinal electric field. Among the various scattering mechanisms which can induce a finite spin-Hall effect we focus on the intrinsic contribution arising from a Rashba-type spin-orbit (RSO) coupling which for couplings linear in momentum usually vanishes. Here we show that non-homogeneity in the spin-orbit coupling arising from structure inversion asymmetry gives rise to a finite spin-Hall effect which we exemplify for a system with striped Rashba spin-orbit coupling