Magneto-optical conductivity and giant Faraday-Kerr rotation in Floquet topological insulators

We study the surface state-dependent magneto-optical properties of an ultrathin Floquet topological insulator (FTI) under the influence of an external perpendicular magnetic field in the terahertz frequency regime. Under the Floquet picture, we treat the circularly polarized off-resonant light as an external perturbation that introduces a mass gap at the Dirac cone, thus, making the surface state Dirac fermions massive. By tuning the optical field energy in the FTI thin-film system, various electronic phase transitions can be driven between the trivial insulator state and the band insulator state. Using Kubo formalism, we derive the real and imaginary parts of the longitudinal and Hall conductivities and demonstrate that these conductivities are sensitively influenced by the strength of the off-resonant optical field, magnetic field, and chemical potentials. On the other hand, topological insulators exhibit strong magneto-optic effects. We further compute the Kerr and Faraday rotation angles and show that giant Kerr and Faraday rotations can be achieved in a FTI thin film by external tuning knobs, such as magnetic and off-resonant optical fields. The Kerr and Faraday rotations in symmetric (top) and antisymmetric (bottom) topological surface states can be controlled for interband and intraband transitions via gate bias voltage. Our results reveal the FTI as an intriguing versatile system whose magneto-optical properties can be effectively tuned optically, magnetically and electrically, thus, uncovering the strong photonics and optoelectronics device application potentials of the FTI.