Some symmetry properties of spin currents and spin polarizations in multi-terminal mesoscopic spin-orbit coupled systems

TL;DR

This paper investigates symmetry properties of spin currents and polarizations in multi-terminal mesoscopic systems with spin-orbit coupling, revealing fundamental constraints and non-conservation phenomena in nonequilibrium conditions.

Contribution

It provides a rigorous theoretical analysis of equilibrium spin properties and highlights the intrinsic non-conservation of nonequilibrium spin currents in such systems.

Findings

No finite equilibrium spin polarization or terminal spin currents in equilibrium.

Nonequilibrium terminal spin currents are generally non-conservative.

Lateral edge spin accumulation may be non-antisymmetric, affecting interpretations of spin Hall effects.

Abstract

We study theoretically some symmetry properties of spin currents and spin polarizations in multi-terminal mesoscopic spin-orbit coupled systems. Based on a scattering wave function approach, we show rigorously that in the equilibrium state no finite spin polarizations can exist in a multi-terminal mesoscopic spin-orbit coupled system (both in the leads and in the spin-orbit coupled region) and also no finite equilibrium terminal spin currents can exist. By use of a typical two-terminal mesoscopic spin-orbit coupled system as the example, we show explicitly that the nonequilibrium terminal spin currents in a multi-terminal mesoscopic spin-orbit coupled system are non-conservative in general. This non-conservation of terminal spin currents is not caused by the use of an improper definition of spin current but is intrinsic to spin-dependent transports in mesoscopic spin-orbit coupled systems. We also show that the nonequilibrium lateral edge spin accumulation induced by a longitudinal charge current in a thin strip of \textit{finite} length of a two-dimensional electronic system with intrinsic spin-orbit coupling may be non-antisymmetric in general, which implies that some cautions may need to be taken when attributing the occurrence of nonequilibrium lateral edge spin accumulation induced by a longitudinal charge current in such a system to an intrinsic spin Hall effect.