Resonant spin Hall conductance in quantum Hall systems lacking bulk and structural inversion symmetry

TL;DR

This paper investigates the resonant spin Hall conductance in quantum wells with spin-orbit interactions under strong magnetic fields, revealing conditions for resonance and effects of symmetry-breaking couplings.

Contribution

It provides detailed calculations of spin Hall conductance considering Rashba and Dresselhaus couplings, and derives conditions for resonance in the presence of both effects.

Findings

Resonant spin Hall conductance occurs at specific magnetic fields due to Landau level degeneracy.

Dresselhaus coupling suppresses the spin Hall resonance.

Resonance leads to a change in quantized charge Hall conductance by 2e^2/h.

Abstract

Following a previous work [Shen, Ma, Xie and Zhang, Phys. Rev. Lett. 92, 256603 (2004)] on the resonant spin Hall effect, we present detailed calculations of the spin Hall conductance in two-dimensional quantum wells in a strong perpendicular magnetic field. The Rashba coupling, generated by spin-orbit interaction in wells lacking bulk inversion symmetry, introduces a degeneracy of Zeeman-split Landau levels at certain magnetic fields. This degeneracy, if occuring at the Fermi energy, will induce a resonance in the spin Hall conductance below a characteristic temperature of order of the Zeeman energy. At very low temperatures, the spin Hall current is highly non-ohmic. The Dresselhaus coupling due to the lack of structure inversion symmetry partially or completely suppresses the spin Hall resonance. The condition for the resonant spin Hall conductance in the presence of both Rashba and Dresselhaus couplings is derived using a perturbation method. In the presence of disorder, we argue that the resonant spin Hall conductance occurs when the two Zeeman split extended states near the Fermi level becomes degenerate due to the Rashba coupling and that the the quantized charge Hall conductance changes by 2e^2/h instead of e^2/h as the magnetic field changes through the resonant field.