Irradiated graphene as a tunable Floquet topological insulator

Abstract

In the presence of a circularly polarized mid-infrared radiation graphene develops dynamical band gaps in itsquasi-energy band structure and becomes a Floquet insulator. Here we analyze how topologically protected edgestates arise inside these gaps in the presence of an edge. Our results show that the gap appearing at̵hΩ~2, where̵hΩis the photon energy, is bridged by two chiral edge states whose propagation direction is set by the directionof the polarization of the radiation field. Therefore, both the propagation direction and the energy window wherethe states appear can be controlled externally. We present both analytical and numerical calculations that fullycharacterize these states. This is complemented by simple topological arguments that account for them and bynumerical calculations for the case of semi-infinite sample, thereby eliminating finite size effects.