Interplay of Floquet engineering and magnetic quantization in topological insulator thin films

We theoretically investigate the magneto-optical properties of topological insulator (TI) thin films under off-resonant circularly polarized light and perpendicular magnetic fields. Using an effective Dirac model with hybridization and Floquet-induced mass terms, we derive the Landau level spectrum for materials like Bi${}_2$Se${}_3$ and Bi${}_2$Te${}_3$. The optical response is computed via the equation-of-motion method, yielding analytical expressions for longitudinal and Hall susceptibilities in both undoped and doped regimes. Numerical results reveal rich absorption spectra from interband and intraband transitions, influenced by temperature, carrier density, light polarization, and Floquet strength. Key features include blue/red spectral shifts, “half-peak” structures, and polarization-induced splitting, which serve as signatures of Floquet band engineering. We find that interband transitions are more sensitive to Floquet interaction than intraband ones, demonstrating the tunability of optical response in light-driven TI systems.