  Silicene (a monolayer of silicon atoms) is a quantum spin Hall insulator
(QSHI), which undergoes a topological phase transition to a band insulator
under external electric field $E_{z}$. We investigate a photo-induced
topological phase transition by irradiating circular polarized light at fixed
$E_{z}$. The band structure and also the topological property are modified by
photon dressing. By increasing the intensity of light at $E_{z}=0 $, a
photo-induced quantum Hall insulator (P-QHI) is realized, where the quantum
Hall effect occurs without magnetic field. Its edge modes are anisotropic
chiral, in which the velocities of up and down spins are different. There
appears a spin polarized metal characterized by topological flat bands at the
critical point between the QSHI and P-QHI. At $E_{z}>E_{\text{cr}}$ with a
certain critical field $E_{\text{cr}}$, a photo-induced spin-polarized quantum
Hall insulator emerge. This is a new state of matter, possessing one Chern
number and one half spin-Chern numbers. The edge mode supports a perfectly
spin-polarized current, which are different from the chiral or helical edge
modes. We newly discovered a single Dirac-cone state along a phase boundary. A
distinctive hallmark of the state is that one of the two Dirac valleys is
closed with a linear dispersion and the other open with a parabolic dispersion.
