Edge states and phase diagram for graphene under polarized light

We investigate the topological phase transitions in graphene under the modulation of circularly polarized light, by analyzing the changes of edge states and its topological structures. A full phase diagram, with up to ten different topological phases, is presented in the parameter space spanned by the driving frequency and light strength. We find that the high-Chern number behavior is very common in the driven system. While the one-photon resonance can create the chiral edge states in the $\pi-$gap, the two-photon resonance will induce the counter-propagating edge modes in the zero-energy gap. When the driving light strength is strong, the number and even the chirality of the edge states may change in the $\pi-$gap. The robustness of the edge states to disorder potential are also examined. We close by discussing the feasibility of experimental proposals.