Spin-Hall edge spin polarization in a ballistic 2D electron system

TL;DR

This paper analyzes the universal properties of the spin-Hall effect in ballistic 2D electron systems, revealing that edge spin polarization is second order in spin-orbit coupling and independent of boundary potential form.

Contribution

It provides an analytical solution confirming the second-order dependence of edge spin polarization on spin-orbit coupling and details the distribution of local spin polarization.

Findings

Net edge spin polarization is proportional to the square of spin-orbit coupling.

Normal and evanescent modes contribute oppositely, canceling in spectral distribution.

Local spin polarization exhibits Friedel oscillations with spin-orbit coupling affecting the oscillation period.

Abstract

Universal properties of spin-Hall effect in ballistic 2D electron systems are addressed. The net spin polarization across the edge of the conductor is second order, ~\lambda^2, in spin-orbit coupling constant independent of the form of the boundary potential, with the contributions of normal and evanescent modes each being ~ \sqrt{\lambda} but of opposite signs. This general result is confirmed by the analytical solution for a hard-wall boundary, which also yields the detailed distribution of the local spin polarization. The latter shows fast (Friedel) oscillations with the spin-orbit coupling entering via the period of slow beatings only. Long-wavelength contributions of evanescent and normal modes exactly cancel each other in the spectral distribution of the local spin density.