Imaging mesoscopic spin Hall flow: Spatial distribution of local spin currents and spin densities in and out of multiterminal spin-orbit coupled semiconductor nanostructures

TLDR

Visualization of phase‑coherent spin flow resolves key issues in understanding mechanisms that generate pure spin Hall currents in ballistic devices. We introduce the concept of bond spin current to describe spin transport between lattice sites in multiterminal spin‑orbit coupled semiconductor nanostructures. The bond spin current is expressed via spin‑dependent nonequilibrium Green functions and applied to compute spatial distributions of microscopic spin currents in a clean, phase‑coherent 2DEG with Rashba SO coupling attached to four leads. Local spin current profiles depend on sample size relative to the spin precession length, establishing this length as the characteristic mesoscale for the spin Hall effect, while disorder reduces the total spin current but bond currents persist throughout the diffusive 2DEG without edge localization.

Abstract

We introduce the concept of bond spin current, which describes the spin transport between two sites of the lattice model of a multiterminal spin-orbit (SO) coupled semiconductor nanostructure, and express it in terms of the spin-dependent nonequilibrium (Landauer-Keldysh) Green functions of the device. This formalism is applied to obtain the spatial distribution of microscopic spin currents in {\em clean} phase-coherent two-dimensional electron gas with the Rashba-type of SO coupling attached to four external leads. Together with the corresponding profiles of the stationary spin density, such visualization of the phase-coherent spin flow allow us to resolve several key issues for the understanding of mechanisms which generate pure spin Hall currents in the transverse leads of ballistic devices due to the flow of unpolarized charge current through their longitudinal leads. The local spin current profiles crucially depend on whether the sample is smaller or greater than the spin precession length, thereby demonstrating its essential role as the characteristic mesoscale for the spin Hall effect in ballistic multiterminal semiconductor nanostructures. Although static spin-independent disorder reduces the magnitude of the total spin current in the leads, the bond spin currents continue to flow through the whole diffusive 2DEG sample, without being localized as edge spin currents around any of its boundaries.