Floquet engineering of gapped 2D materials

It is demonstrated theoretically that the interaction of gapped 2D materials (gapped graphene and transition metal dichalchogenide monolayers) with a strong high-frequency electromagnetic field (dressing field) crucially changes the band structure of the materials. As a consequence, the renormalized band structure of the materials drastically depends on the field polarization. Particularly, a linearly polarized dressing field always decreases band gaps, whereas a circularly polarized field breaks the equivalence of band valleys in different points of the Brillouin zone and can both increase and decrease corresponding band gaps. It is shown also that a dressing field can turn both the band gaps and the spin splitting of the bands into zero. As a result, the dressing field can serve as an effective tool to control spin and valley properties of the materials in various optoelectronic applications.