  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.
