Universal edge bands induced by linearly polarized irradiation on phosphorene

Phosphorene (a monolayer of black phosphorus) is a large gap semiconductor with high mobility and has great application potential. Numerical calculations reveal that phosphorene is a topologically trivial material and can only host edge bands on specified edges such as the zigzag edge. A linearly polarized irradiation on the phosphorene lattice results in the dynamic gaps in the quasi-energy spectrum. We found that the irradiation polarized in the zigzag direction induces new edge bands within the dynamic gaps on any type of edge (zigzag, armchair, or other bearded edge). We proposed a new gauge independent quantity, $\delta +g$ , to account for the appearence of universal edge bands, where δ is the detune and g is the light induced valence-conduction band transition element. The number of edge bands in the dynamic gaps is reflected by the winding number of it.