The emergence of photo-induced topological phases and their phase transitions are theoretically predicted in organic salt $alpha$-(BEDT-TTF)$_2$I$_3$, which possesses inclined Dirac cones in its band structure. By analyzing a photo-driven tight-binding model describing conduction electrons in the BEDT-TTF layer using the Floquet theorem, we demonstrate that irradiation with circularly polarized light opens a gap at the Dirac points, and the system eventually becomes a Chern insulator characterized by a quantized topological invariant. A rich phase diagram is obtained in plane of amplitude and frequency of light, which contains Chern insulator, semimetal, and normal insulator phases. We find that the photo-induced Hall conductivity provides a sensitive means to detect the predicted phase evolutions experimentally. This work contributes towards developing the optical manipulation of electronic states in matter through broadening the range of target materials that manifest photo-induced topological phase transitions.
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