  Spin-Hall conductivity (SHC) of fully relativistic (4x4 matrix) Dirac
electrons is studied based on the Kubo formula aiming at possible application
to bismuth and bismuth-antimony alloys. It is found that there are two distinct
contributions to SHC, one only from the states near the Fermi energy and the
other from all the occupied states. The latter remains even in the insulating
state, i.e., when the chemical potential lies in the band-gap, and turns to
have the same dependences on the chemical potential as the orbital
susceptibility (diamagnetism), a surprising fact. These results are applied to
bismuth-antimony alloys and the doping dependence of the SHC is proposed.
