Spin and charge shot noise in mesoscopic spin Hall systems

Abstract

Injection of unpolarized charge current through the longitudinal leads of a four-terminal two-dimensional electron gas with the Rashba spin-orbit (SO) coupling and SO scattering off extrinsic impurities is responsible not only for the pure spin Hall current in the transverse leads, but also for non-equilibrium random time-dependent current fluctuations. We employ the scattering approach to current-current correlations in multiterminal nanoscale conductors to analyze the shot noise of transverse pure spin Hall current and zero charge current, or transverse spin current and non-zero charge Hall current, driven by unpolarized or spin-polarized injected longitudinal charge current, respectively. Since any spin-flip acts as an additional source of noise, we argue that these shot noises provide a unique experimental tool to differentiate between intrinsic and extrinsic SO mechanisms underlying the spin Hall effect in paramagnetic devices.