Semiclassical theory of spin transport in spin-orbit coupled systems

TL;DR

This paper develops a semiclassical framework for understanding spin transport in systems with spin-orbit coupling, accounting for various contributions to spin current and matching quantum predictions for spin-Hall conductivity.

Contribution

It introduces a comprehensive semiclassical theory of spin transport that includes spin and torque dipole effects, aligning with quantum calculations for spin-Hall conductivity.

Findings

Derived an expression for intrinsic spin-Hall conductivity in hole-doped semiconductors.

Highlighted the significance of torque dipole moments in spin accumulation near boundaries.

Validated the semiclassical approach against the Kubo formula predictions.

Abstract

Motivated by recent interest in novel spintronics effects, we develop a semiclassical theory of spin transport that is valid for spin-orbit coupled bands. Aside from the obvious convective term in which the average spin is transported at the wavepacket group velocity, the spin current has additional contributions from the wavepacket's spin and torque dipole moments. Electric field corrections to the group velocity and carrier spin contribute to the convective term. Summing all terms we obtain an expression for the intrinsic spin-Hall conductivity of a hole-doped semiconductor, which agrees with the Kubo formula prediction for the same quantity. We discuss the calculation of spin accumulation, which illustrates the importance of the torque dipole near the boundary of the system.