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We investigate the effect of a high-frequency electromagnetic field with both circular and linear polarization on the emergence of quantum phases in thin topological insulators. Simultaneously, the influence of the system parameters (such as the magnetic impurity, thickness engineering, and structural inversion asymmetry of the
potential) on the emergence of topological phases is studied. We focus our attention on the high-frequency
regime in which it is possible to consider an expansion for the Floquet Hamiltonian in terms of orders of 1/\Omega. The topological invariants are determined and it is demonstrated that some phase transitions between the quantum anomalous Hall insulator, quantum pseudospin Hall insulator, quantum spin Hall insulator, and normal insulator can be induced by altering the aforementioned parameters of the system. To avoid the heating process, tuning of the system parameters gives us the opportunity to observe these phase transitions at low intensities of light.
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