Intrinsic Spin Hall Effect in the presence of Extrinsic Spin-Orbit Scattering

TL;DR

This paper develops a unified theoretical framework for intrinsic and extrinsic spin Hall effects in 2D electron and hole systems with Rashba spin-orbit coupling, revealing surprising non-analytic behavior in electrons.

Contribution

It provides a combined analytical theory for intrinsic and extrinsic spin Hall effects, highlighting novel non-analytic phenomena in 2D electron systems with Rashba coupling.

Findings

Additive result for 2D holes' spin Hall conductivity

Non-analyticity in 2D electrons' spin Hall response as Rashba coupling approaches zero

Discussions relate theoretical predictions to experimental observations

Abstract

Intrinsic and extrinsic spin Hall effects are considered together on an equal theoretical footing for the Rashba spin-orbit coupling in two-dimensional (2D) electron and hole systems, using the diagrammatic method for calculating the spin Hall conductivity. Our analytic theory for the 2D holes shows the expected lowest-order additive result for the spin Hall conductivity. But, the 2D electrons manifest a very surprising result, exhibiting a non-analyticity in the Rashba coupling strength $\alpha$ where the strictly extrinsic spin Hall conductivity (for $\alpha = 0$) cannot be recovered from the $\alpha \to 0$ limit of the combined theory. The theoretical results are discussed in the context of existing experimental results.