Orbital ac spin-Hall effect in the hopping regime

TL;DR

This paper demonstrates that Rashba and Dresselhaus spin-orbit interactions induce a frequency-dependent spin-Hall effect in localized electrons, with implications for spin transport at low temperatures and in the hopping regime.

Contribution

It reveals how spin-orbit interactions cause a spin-Hall effect in the hopping regime, including the role of phonons and interference effects, extending understanding of spin transport in localized systems.

Findings

Spin-Hall conductivity is proportional to ω^2 at zero temperature.

Phonon coupling introduces an imaginary component proportional to ω.

Persistent spin currents can exist at thermal equilibrium without an external electric field.

Abstract

The Rashba and Dresselhaus spin-orbit interactions are both shown to yield the low temperature spin-Hall effect for strongly localized electrons coupled to phonons. A frequency-dependent electric field ${\bf E}(\omega)$ generates a spin-polarization current, normal to ${\bf E}$, due to interference of hopping paths. At zero temperature the corresponding spin-Hall conductivity is real and is proportional to $\omega^{2}$. At non-zero temperatures the coupling to the phonons yields an imaginary term proportional to $\omega$. The interference also yields persistent spin currents at thermal equilibrium, at ${\bf E}=0$. The contributions from the Dresselhaus and Rashba interactions to the interference oppose each other.