Spin and Charge Shot Noise in Mesoscopic Spin Hall Systems

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/or SO scattering off extrinsic impurities is responsible not only for the pure spin Hall current in the transverse leads, but also for 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 and zero charge current, or transverse spin current and non-zero charge Hall current, driven by unpolarized or spin-polarized longitudinal current, respectively. Since any spin-flip acts as an additional source of noise, we argue that these shot noises offer a unique tool to differentiate between intrinsic and extrinsic SO mechanisms underlying the spin Hall effect in paramagnetic devices.