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We study the photon-dressed electronic band structure of topological insulator thin films doped by magnetic impurities in response to an off-resonance time-periodic electromagnetic field. The thin films irradiated by a circularly polarized light undergo phase transitions, and a fascinating feature of distinct phases emerges in the phase diagram depending on the frequency, intensity, and polarization of the light. As a particular case, the quantum anomalous Hall insulator phase is induced purely by the light-induced mass term with no need for any external magnetic field or even magnetization arising from doping magnetic impurities. Moreover, a quantum pseudo-spin Hall insulator (QPHI) phase emerges in the phase diagram, leading to anisotropic helical edge states with zero total Chern number. We verify these achievements by numerical calculations for a nanoribbon of the thin film for which the edge mode behavior is observed at several points on the phase diagram. The emergence of the mentioned topological phases and the edge modes are further confirmed by both calculating the Hall conductivity by means of the Kubo formula and the Chern number of each band. The effect of light parameters on the Landau-level fan diagram in the presence of a perpendicular magnetic field indicates various topological phases occurring at higher Chern numbers.
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