  We investigate the intrinsic spin Hall effect in two-dimensional electron
gases in quantum wells with two subbands, where a new intersubband-induced
spin-orbit coupling is operative. The bulk spin Hall conductivity
$\sigma^z_{xy}$ is calculated in the ballistic limit within the standard Kubo
formalism in the presence of a magnetic field $B$ and is found to remain finite
in the B=0 limit, as long as only the lowest subband is occupied. Our
calculated $\sigma^z_{xy}$ exhibits a nonmonotonic behavior and can change its
sign as the Fermi energy (the carrier areal density $n_{2D}$) is varied between
the subband edges. We determine the magnitude of $\sigma^z_{xy}$ for realistic
InSb quantum wells by performing a self-consistent calculation of the
intersubband-induced spin-orbit coupling.
