Entropy Driven Inductive Response of Topological Insulators

3D topological insulators (3DTIs) are characterized by an insulating bulk and extended surface states exhibiting a helical spin texture. In this work, we investigate the hyperfine interaction between the spin-charge coupled transport of electrons and the nuclear spins in these surface states. Previous work has shown that in the quantum spin Hall insulator phase, work can be extracted from a bath of polarized nuclear spins as a resource [1]. We employ nonequilibrium Green’s function analysis to show that a similar effect exists on the surface of a 3D topological insulator, albeit rescaled by the ratio between electronic mean free path and device length. The induced current due to thermal relaxation of polarized nuclear spins has an inductive nature. We emphasize this by rewriting the current-voltage relation in harmonic response as a lumped element model containing two parallel resistors and an inductor. An efficiency estimate follows from comparing the spin-flip induced current to the Ohmic contribution. The inductive effect is most prominent in topological insulators which have a large number of spinful nuclei per coherent segment, consisting of mean free path length, Fermi wavelength and penetration depth of the surface state.