Shot Noise of Spin-Decohering Transport in Spin-Orbit Coupled Nanostructures

TL;DR

This paper extends the scattering theory of quantum shot noise to include spin-density matrices, revealing how spin decoherence affects charge fluctuations in spin-orbit coupled nanostructures, with implications for measuring spin coherence.

Contribution

It introduces a formalism for spin-resolved shot noise in quantum-coherent nanostructures with spin interactions, linking shot noise to spin decoherence and phase coherence.

Findings

Spin decoherence enhances shot noise and Fano factors in diffusive wires.

Narrow wires suppress shot noise increase, preserving phase coherence.

Fano factor correlates with spin polarization, measuring spin coherence.

Abstract

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 various 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 (SO) spin-orbit 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 $F_{\uparrow \to \uparrow \downarrow}$ 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 $F_{\uparrow \to \uparrow \downarrow}$.