  The kinetics of the extrinsic spin Hall conductivity induced by the skew
scattering is performed from the fully microscopic kinetic spin Bloch equation
approach in $(001)$ GaAs symmetric quantum well. In the steady state, the
extrinsic spin Hall current/conductivity vanishes for the linear-$\mathbf k$
dependent spin-orbit coupling and is very small for the cubic-$\mathbf k$
dependent spin-orbit coupling. The spin precession induced by the
Dresselhaus/Rashba spin-orbit coupling plays a very important role in the
vanishment of the extrinsic spin Hall conductivity in the steady state. An
in-plane spin polarization is induced by the skew scattering, with the help of
the spin-orbit coupling. This spin polarization is very different from the
current-induced spin polarization.
