Generation of spin currents and spin densities in systems with reduced symmetry

TL;DR

This paper explores how reduced symmetry in semiconductor crystals leads to complex spin-current responses to electric fields, challenging previous assumptions and providing a systematic framework to distinguish spin currents and densities.

Contribution

It introduces a comprehensive theory for spin-current responses in low-symmetry systems, clarifying the roles of intrinsic/extrinsic contributions and vertex corrections.

Findings

Non-spin-Hall components can appear in low-symmetry systems.

The distinction between intrinsic and extrinsic spin currents is not always meaningful.

A systematic method to differentiate spin currents and densities in experiments.

Abstract

We show that the spin-current response of a semiconductor crystal to an external electric field is considerably more complex than previously assumed. While in systems of high symmetry only the spin-Hall components are allowed, in systems of lower symmetry other non-spin-Hall components may be present. We argue that, when spin-orbit interactions are present only in the band structure, the distinction between intrinsic and extrinsic contributions to the spin current is not useful. We show that the generation of spin currents and that of spin densities in an electric field are closely related, and that our general theory provides a systematic way to distinguish between them in experiment. We discuss also the meaning of vertex corrections in systems with spin-orbit interactions.