Conductivity oscillation of surface state of three-dimensional topological insulators induced by a linearly polarized terahertz field

We have theoretically studied the longitudinal dc conductivity of the surface state of three-dimensional (3D) topological insulators (TIs) under a linearly polarized (LP) terahertz (THz) field irradiation via the Floquet theory and Green's function technique. It was found that, due to the anisotropic quasienergy spectrum under the LP light, the longitudinal conductivities parallel and perpendicular to the polarized direction of the LP light are not the same. When the 3D TI's chemical potential is zero, both of the conductivities undergo an oscillation against the electron-field interaction parameter because of the contribution of the photon modulated side-band transport at different position. The oscillation is dramatically suppressed when the chemical potential is higher or lower than zero. There is a pronounced dip in the dc conductivity at a specific field frequency twice the chemical potential, which can be seen as a gap-induced metal-to-insulator transition of the surface state of 3D TIs. As the dc conductivity of the surface state of 3D TIs has such a pronounced response to the LP THz field, our investigations involving the interaction between TIs and LP THz field actually provided the possibility of TI application in THz devices.