Spin Hall Current Driven by Quantum Interferences in Mesoscopic Rashba Rings

We propose an all-electrical nanoscopic structure where {\em pure} spin current is induced in the transverse voltage probes attached to {\em quantum-coherent} one-dimensional ring when conventional unpolarized charge current is injected through its longitudinal leads. Tuning of the Rashba spin-orbit coupling in semiconductor heterostructure hosting the ring generates quasi-periodic oscillations of the predicted spin Hall current due to {\em spin-sensitive quantum-interference effects} caused by the difference in Aharonov-Casher phase acquired by opposite spins states traveling clockwise and counterclockwise. Its amplitude is comparable to the mesoscopic spin Hall current predicted for finite-size two-dimensional electron gases, while it gets reduced in wide two-dimensional or disordered rings.