Spin dynamics and persistent currents on a cylindrical surface of topological insulator

Spin dynamics and persistent charge and spin currents of an electron on a cylindrical surface of a topological insulator are investigated. We find that the cylindrical symmetry of topological insulator leads to opening a band gap in the energy spectrum of the topological surface states of the system depending on the radius of the cylinder. In addition, the spectrum acquires a shift in the aforementioned symmetry. The numerical analysis of the dynamical equations obtained from the Heisenberg equation of motion shows that the precession of the tangential, radial, and longitudinal components of the spin transport is very small, reflecting the robustness of the conducting metallic surface states of topological insulators. Moreover, the persistent charge current on the cylindrical surface of TI vanishes, as expected in the absence of any time-reversal symmetry breaking perturbation. On the other hand, the longitudinal component of the persistent spin-polarized current remains constant in the course of electron dynamics on the cylindrical surface, whereas its x- and y-components oscillate with finite phase shift