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We theoretically study the real-time dynamics of the photoinduced topologicalphase transition to a nonequilibrium Floquet Chern insulator in an organicconductor $\alpha$-(BEDT-TTF)$_2$I$_3$, which was recently predicted using theFloquet theory. By using a tight-binding model of $\alpha$-(BEDT-TTF)$_2$I$_3$that hosts a pair of tilted Dirac-cone bands at the Fermi level, we solve thetime-dependent Schr\"odinger equation and obtained time evolutions of physicalquantities for continuous-wave and pulse excitations with circularly polarizedlight. We demonstrate that, for the continuous-wave excitations, time profilesof the Chern number and the Hall conductivity show indications of the Floquettopological insulator. We argue that the Hall conductivity exhibits a slowoscillation with its frequency corresponding to a photoinduced direct gapdetermined by the Floquet band structure. With pulse excitations, transientexcitation spectra are obtained, from which we infer the formation of Floquetbands and the gap opening at the Dirac point during the pulse irradiation. Thisdynamical gap formation is also manifested by the slow oscillation component ofthe Hall conductivity; that is, its frequency increases with time toward thepulse peak at which it nearly coincides with the photoinduced direct gap. Therelevance of the results to experiments is also discussed.

physical review. b./physical review. b

Real-time dynamics of the photoinduced topological state in organic  conductor $\alpha$-(BEDT-TTF)$_2$I$_3$ under continuous-wave and pulse  excitations