  The spin Hall effect in a two-dimensional electron system on honeycomb
lattice with both intrinsic and Rashba spin-orbit couplings is studied
numerically. Integer quantized spin Hall conductance is obtained at zero Rashba
coupling limit when electron Fermi energy lies in the energy gap created by the
intrinsic spin-orbit coupling, in agreement with recent theoretical prediction.
While nonzero Rashba coupling destroys electron spin conservation, the spin
Hall conductance is found to remain near the quantized value, being insensitive
to disorder scattering, until the energy gap collapses with increasing the
Rashba coupling. We further show that the charge transport through
counterpropagating spin-polarized edge channels is well quantized, which is
associated with a topological invariant of the system.
