What can we learn about the dynamics of transported spins by measuring shot noise in spin–orbit-coupled nanostructures?

We review recent studies of the shot noise of spin-polarized charge currents and pure spin currents in multiterminal semiconductor nanostructures, while focusing on the effects brought by the intrinsic Rashba spin–orbit (SO) coupling and/or extrinsic SO scattering off impurities in two-dimensional electron gas (2DEG) based devices. By generalizing the scattering theory of quantum shot noise to include the full spin-density matrix of electrons injected from a spin-filtering electrode, we show how decoherence and dephasing in the course of spin precession can lead to the substantial enhancement of the Fano factor (noise-to-current ratio) of spin-polarized charge currents. These processes are suppressed by decreasing the width of the diffusive Rashba wire, so that purely electrical measurement of the shot noise in a ferromagnet|SO-coupled-diffusive-wire|paramagnet setup can quantify the degree of quantum coherence of transported spin through a remarkable one-to-one correspondence between the purity of the spin state and the Fano factor. In four-terminal SO-coupled nanostructures, injection of unpolarized charge current through the longitudinal leads is responsible not only for the pure spin Hall current in the transverse leads, but also for nonequilibrium random time-dependent current fluctuations. The analysis of 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, reveals a unique experimental tool to differentiate between the intrinsic Rashba and extrinsic SO mechanisms underlying the spin Hall effect in 2DEG devices. When the intrinsic mechanisms responsible for spin precession start to dominate the spin Hall effect, they also enhance the shot noise of transverse spin and charge transport in multiterminal geometries. Finally, we discuss the shot noise of transverse spin and zero charge currents in the quantum-interference-driven spin Hall effect in ballistic four-terminal Aharonov–Casher rings realized using high-mobility 2DEG with the Rashba SO coupling. The modulation of the Rashba coupling by the gate electrode imprints the oscillatory signature of constructive and destructive spin interference around the ring on both the spin and charge shot noise, which differ from the corresponding oscillations of the spin Hall conductance, thereby revealing quantum-interference-driven temporal correlations between spin-resolved charge currents of opposite spins.