  The intrinsic spin Hall conductivity of typical topological insulators
Sb$_2$Se$_3$, Sb$_2$Te$_3$, Bi$_2$Se$_3$, and Bi$_2$Te$_3$ in the bulk form, is
calculated from first-principles by using density functional theory and the
linear response theory in a maximally localized Wannier basis. The results show
that there is a finite spin Hall conductivity of 100--200 ($\hbar$/2e)(S/cm) in
the vicinity of the Fermi energy. Although the resulting values are an order of
magnitude smaller than that of heavy metals, they show a comparable spin Hall
angle due to their relatively lower longitudinal conductivity. The spin Hall
angle for different compounds are then compared to that of recent experiments
on topological-insulator/ferromagnet heterostructures. The comparison suggests
that the role of the bulk in generating a spin current and consequently a spin
torque in magnetization switching applications is comparable to that of the
surface including the spin-momentum locked surface states and the
Rashba-Edelstein effect at the interface.
