Spin transistor action from Onsager reciprocity and SU(2) gauge theory

TL;DR

This paper demonstrates how SU(2) spin-orbit interactions can be effectively mapped to U(1) gauge fields in confined systems, revealing conditions for spin conductance and its control via symmetry breaking, supported by numerical simulations.

Contribution

It introduces a gauge transformation framework that simplifies SU(2) spin-orbit Hamiltonians to U(1) forms and analyzes spin conductance behavior using Onsager relations.

Findings

Spin conductance vanishes in two-terminal setups due to Onsager reciprocity.

Weak symmetry breaking or additional terminals enable spin conductance.

Numerical simulations confirm theoretical predictions for mesoscopic systems.

Abstract

We construct a local gauge transformation to show how, in confined systems, a generic, weak nonhomogeneous SU(2) spin-orbit Hamiltonian reduces to two U(1) Hamiltonians for spinless fermions at opposite magnetic fields, to leading order in the spin-orbit strength. Using an Onsager relation, we further show how the resulting spin conductance vanishes in a two-terminal setup, and how it is turned on by either weakly breaking time-reversal symmetry or opening additional transport terminals. We numerically check our theory for mesoscopic cavities as well as Aharonov-Bohm rings.