Intrinsic spin Hall effect in topological insulators: A first-principles study

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