  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.
