  We study spin-Hall effects in time-reversal symmetry (TRS) broken systems
such as triplet chiral superconductors and TRS preserved ones such as graphene.
For chiral triplet superconductors, we show that the edge states carry a
quantized spin-Hall current in response to an applied Zeeman magnetic field $B$
along the ${\bf d}$ vector \cite{leggett1}, whereas the edge spin-current for
${\bf B} \perp {\bf d}$ is screened by the condensate. We also derive the bulk
spin-Hall current for chiral triplet superconductors for arbitrary relative
orientation of ${\bf B}$ and ${\bf d}$ and discuss its relation with the edge
spin-current. For TRS invariant system graphene, we show that the bulk
effective action, unlike its TRS broken counterparts, does not support a SU(2)
Hopf term but allows a crossed Hopf term in the presence of an external
electromagnetic field, which yields a quantized bulk spin-Hall current in
response to an electric field. We also present an analytical solution of the
edge problem for armchair edges of graphene and contrast the properties of
these edge states with their time reversal symmetry broken counterparts in
chiral superconductors. We propose possible experiments to test our results.
