  We investigate spin transport of heavy holes in III-V semiconductor quantum
wells in the presence of spin-orbit coupling of the Rashba type due to
structure-inversion asymmetry. Similarly to the case of electrons, the
longitudinal spin conductivity vanishes, whereas the off-diagonal elements of
the spin-conductivity tensor are finite giving rise to an intrinsic spin-Hall
effect. For a clean system we find a closed expression for the spin-Hall
conductivity depending on the length scale of the Rashba coupling and the hole
density. In this limit the spin-Hall conductivity is enhanced compared to its
value for electron systems, and it vanishes with increasing strength of the
impurity scattering. As an aside, we also derive explicit expressions for the
Fermi momenta and the densities of holes in the different dispersion branches
as a function of the spin-orbit coupling parameter and the total hole density.
These results are of relevance for the interpretation of possible Shubnikov-de
Haas measurements detecting the Rashba spin splitting.
