The Non-Dissipative Spin-Hall Current

TL;DR

This paper presents a theoretical model explaining the non-dissipative Spin-Hall current using Aharonov-Bohm effects in momentum space, deriving an exact conductivity value and analyzing the impact of scattering potentials.

Contribution

It introduces a novel theory based on momentum-space Aharonov-Bohm effects for Spin-Hall conductivity, providing exact calculations and insights into scattering effects.

Findings

Exact Spin-Hall conductivity value of e/4π derived.

Non-commutative coordinate relations due to Aharonov-Bohm vortex.

Spin-Hall current vanishes under time reversal scattering in infinite systems.

Abstract

A theory based on the Aharonov -Bohm effect in the momentum space for the Spin-Hall conductivity without a magnetic field is presented. The two dimensional Rashba Hamiltonian is diagonalized in the momentum spinor basis. This spinor is singular at K=0. The representation of the cartesian coordinates in the spinor momentum basis obey non-commutative rules. The non-commuting relations are a result of an effective Aharonov-Bohm vortex at K=0. We find the exact value of $\frac{e}{4\pi}$ for the Spin-Hall conductivity. The effect of a time reversal scattering potential on the Spin-Hall current causes the current to vanishes for an infinite system.