Photoinduced state of Floquet insulator in graphene-like crystal

Floquet spectrum of charge carriers in a 2D-crystal with initially displaced Dirac points has been derived. The phase and amplitude dependences of the energy gap induced by elliptically polarized and bichromatic high-frequency fields has been investigated. In contrast to graphene the linearly polarized electric field has been shown to be able to transform the initially semi-metallic state of Dirac crystal into the Floquet-insulator state. The conditions for such a transition are indicated, one of which is the mismatch between the orientation of the field polarization line and the direction of the crystallographic axes.