  Photoinduced phase transitions and charge dynamics in the interacting
Dirac-electron system with a charge-ordered ground state are theoretically
studied by taking an organic salt $\alpha$-(BEDT-TTF)$_2$I$_3$. By analysing
the extended Hubbard model for this compound using a combined method of
numerical simulations based on the time-dependent Schr\"odinger equation and
the Floquet theory, we observe successive dynamical phase transitions from the
charge-ordered insulator to a gapless Dirac semimetal and, eventually, to a
Chern insulator phase under irradiation with circularly polarized light. These
phase transitions occur as a consequence of two major effects of circularly
polarized light, i.e., closing of the charge gap through melting the charge
order and opening of the topological gap by breaking the time reversal symmetry
at the Dirac points. We demonstrate that these photoinduced phenomena are
governed by charge dynamics of driven correlated Dirac electrons.
