Perfect inverse spin Hall effect and inverse Edelstein effect due to helical spin-momentum locking in topological surface states

We present a theory for the inverse spin Hall effect in a thin film of topological insulator (TI) ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, connected to a reservoir with applied spin bias, in the ballistic regime. In the case that either the spin polarization of the spin bias is along the longitudinal direction, or the hybridization gap $\mathrm{\ensuremath{\Delta}}$ of the surface states vanishes, the spin Hall angle ${\mathrm{\ensuremath{\Theta}}}_{\mathrm{sh}}$ tends to infinity, indicating that the spin bias is perfectly converted into a measurable transverse charge current, essentially without generating a longitudinal spin current in the TI. In other cases, with increasing the Fermi energy ${E}_{\mathrm{F}}$ from the bottom of the conduction band of surface states, ${\mathrm{\ensuremath{\Theta}}}_{\mathrm{sh}}$ grows continuously from zero and exhibits an interesting linear dependence on ${E}_{\mathrm{F}}/\mathrm{\ensuremath{\Delta}}$ for ${E}_{\mathrm{F}}\ensuremath{\gg}\mathrm{\ensuremath{\Delta}}$. We also find that the inverse Edelstein effect occurs, when the in-plane transverse component of the spin polarization vector is nonzero. The spin-to-charge conversion becomes complete, when the spin polarization vector is along the transverse direction, or the hybridization gap $\mathrm{\ensuremath{\Delta}}$ vanishes.