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

Abstract

A previous work [Shen, Ma, Xie, and Zhang, Phys. Rev. Lett. 92, 256603 (2004)] on two-dimensional quantum wells with Rashba type spin-orbit interaction under a strong perpendicular magnetic field is generalized to include the Dresselhaus coupling. The Rashba coupling and the Dresselhaus coupling interplay with the Zeeman effect in opposing ways. The former tends to produce a resonant spin Hall effect at certain magnetic fields while the latter suppresses it. Due to the resonant spin Hall effect, the spin Hall current is highly nonohmic at low temperatures. 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 become degenerate due to the Rashba coupling, and that the quantized charge Hall conductance changes by $2{e}^{2}∕h$ instead of ${e}^{2}∕h$ as the magnetic field changes through the resonant field.