Shot noise of spin-polarized charge currents as a probe of spin coherence in spin-orbit coupled nanostructures

We generalize the scattering theory of quantum shot noise to include the full spin-density matrix of electrons injected from a spin filtering or ferromagnetic electrode into a quantum-coherent nanostructure governed by arbitrary spin-dependent interactions. This formalism yields the spin-resolved shot noise power for different experimental measurement setups—with ferromagnetic source and ferromagnetic or normal drain electrodes— whose evaluation for the diffusive multichannel quantum wires with the Rashba spin-orbit SO coupling shows how spin decoherence and dephasing lead to substantial enhancement of charge current fluctuations characterized by Fano factors 1/3 . However, these processes and the corresponding shot-noise increase are suppressed in narrow wires, so that charge transport experiments measuring the Fano factor F↑→↑↓ in a ferromagnet/SO-coupled-wire/paramagnet setup also quantify the degree of phase coherence of transported spin—we predict a one-to-one correspondence between the magnitude of the spin-polarization vector and F↑→↑↓.