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 intrinsic Rashba spin-orbit (SO) coupling and/or extrinsic SO scattering off impurities. 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 spin decoherence and dephasing lead to 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 phase-coherence of transported spin through a remarkable one-to-one correspondence between the purity of the spin state and the Fano factor. In the 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 intrinsic Rashba and extrinsic SO mechanisms underlying the spin Hall effect in two-dimensional electron gas (2DEG) devices. The intrinsic mechanisms are found to enhance the shot noise through spin precession. Finally, we discuss the shot noise of transverse spin and zero charge current in the quantum-interference-driven spin Hall effect in four-terminal Aharonov-Casher rings realized using 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 correlations between spin-resolved currents of opposite spins. PACS numbers: 72.25.Dc,73.23.-b,05.40.Ca,03.65.Vf, 03.65.Yz Shot noise in spin-orbit-coupled nanostructures 2