Topologically trivial and nontrivial edge bands in graphene induced by irradiation

•A minimal model is proposed to describe the Floquet band structure of two-dimensional materials with light-induced resonant inter-band transition.•New edge bands are found in the resonant gap of zigzag and armchair graphene ribbons under linearly polarized irradiation.•Chern number of Floquet bands is reduced into winding number at resonance.

We proposed a minimal model to describe the Floquet band structure of two-dimensional materials with light-induced resonant inter-band transition. We applied it to graphene to study the band features caused by the light irradiation. Linearly polarized light induces pseudo gaps (gaps are functions of wavevector), and circularly polarized light causes real gaps on the quasi-energy spectrum. If the polarization of light is linear and along the longitudinal direction of zigzag ribbons, flat edge bands appear in the pseudo gaps, and if it is in the lateral direction of armchair ribbons, curved edge bands can be found. For the circularly polarized cases, edge bands arise and intersect in the gaps of both types of ribbons. The edge bands induced by the circularly polarized light are helical and those by linearly polarized light are topologically trivial ones. The Chern number of the Floquet band, which reflects the number of pairs of helical edge bands in graphene ribbons, can be reduced into the winding number at resonance.