Hybridization effects on persistent currents in rings of topological insulators

We investigate spin dynamics and persistent charge and spin currents of electrons in rings of Topological Insulator (TI) thick and ultrathin films. Interesting effects are observed, in particular, precession of the tangential and longitudinal components of the spin transport is very small, while the radial component does not precess and thus behaves as a conserved quantity in the system dynamics. Further, we find that persistent charge current vanishes due to the equal and opposite contributions of the clockwise and counterclockwise propagating modes, whereas longitudinal spin polarized current vanishes due to the inversion symmetry along the cylindrical axis in both cases. Strikingly, the x- and y-components of spin polarized current oscillate with finite phase shift in the ring of thick film, whereas they vanish in the ring of ultrathin film due to the cancellation of antiparallel spin polarizations of the counterclockwise and clockwise propagating modes originated from the hybridization between the topologically protected conducing states of the outer and inner surfaces of the ring.