Conserved spin Hall conductance in two dimensional electron gas in a perpendicular magnetic field

TL;DR

This paper studies the spin Hall effect in a two-dimensional electron gas under a perpendicular magnetic field, revealing that spin-orbit coupling and Zeeman splitting cause resonances that enhance the total spin Hall conductance.

Contribution

It demonstrates that the conserved spin current exhibits resonances due to Landau level degeneracies, leading to an overall enhancement of the spin Hall conductance in magnetic fields.

Findings

Resonances occur at certain magnetic fields due to Landau level degeneracies.

Both conventional and torque dipole components of spin conductance have the same sign.

Torque dipole correction dominates near resonances.

Abstract

Using the microscopic theory of the conserved spin current [Phys. Rev. Lett. \textbf{96}, 076604 (2006)], we investigate the spin Hall effect in the two dimensional electron gas system with a perpendicular magnetic field. The spin Hall conductance $\sigma_{\mu\nu}^{s}$ as a response to the electric field consists of two parts, i.e., the conventional part $\sigma_{\mu\nu}^{s0}$ and the spin torque dipole correction $\sigma_{\mu\nu}^{s\tau}$. It is shown that the spin-orbit coupling competes with Zeeman splitting by introducing additional degeneracies between different Landau levels at certain values of magnetic field. These degeneracies, if occurring at the Fermi level, turn to give rise to resonances in both $\sigma_{\mu\nu}^{s0}$ and $\sigma_{\mu\nu }^{s\tau}$ in spin Hall conductance. Remarkably, both of these two components have the same sign in the wide range of variation in the magnetic field, which result in an overall enhancement of the total spin Hall current. In particular, the magnitude of $\sigma_{\mu\nu}^{s\tau}$ is much larger than that of $\sigma_{\mu\nu}^{s0}$ around the resonance.