  Spin current and accumulation generated by the electric field in spin Hall
insulator (SHI) are investigated theoretically in terms of the Keldysh
formalism. In contrast to the quantum Hall system, there are no massless edge
modes in general. The spin current is generated near the contacts to the
electrodes by the hybridization between the metallic states and the
conduction/valence bands of the SHI, but is truncated by the sink and source of
the spin. However, one can produce the spin current flowing out to the
conductors, which is attached to the SHI, and also the spin accumulation there
due to the leakage charge current which breaks the time-reversal symmetry.
