Magneto-spin Hall conductivity of a two-dimensional electron gas

TL;DR

This paper investigates how disorder and magnetic fields induce out-of-plane spin polarization and spin Hall conductivity in a 2D electron gas with Rashba spin-orbit coupling, using diagrammatic and Green function methods.

Contribution

It demonstrates the emergence of spin polarization and spin Hall effects due to disorder and magnetic fields in a 2D electron gas with Rashba coupling, extending results from clean to disordered regimes.

Findings

Out-of-plane spin polarization is induced by in-plane magnetic fields.

Finite spin Hall conductivity arises from the interplay of disorder and magnetic fields.

Results are valid across the full disorder parameter range.

Abstract

It is shown that the interplay of long-range disorder and in-plane magnetic field gives rise to an out-of-plane spin polarization and a finite spin Hall conductivity of the two-dimensional electron gas in the presence of Rashba spin-orbit coupling. A key aspect is provided by the electric-field induced in-plane spin polarization. Our results are obtained first in the \textit{clean} limit where the spin-orbit splitting is much larger than the disorder broadening of the energy levels via the diagrammatic evaluation of the Kubo-formula. Then the results are shown to hold in the full range of the disorder parameter $\alpha p_F \tau$ by means of the quasiclassical Green function technique.