Floquet Modification of the Bandgaps and Energy Spectrum in Flat-Band Pseudospin-1 Dirac Materials

In this paper, we investigate the so-called electronic dressed states, a unified quasiparticle resulting from the interaction between electrons in a two-dimensional material with an off-resonance optical dressing field. If the frequency of this field is much larger than all characteristic energies in the system, such as the Fermi energy or bandgap(s), the electronic band structure is affected by radiation so that some important properties of the electron dispersions could be modified in a way desirable for practical applications. For example, circularly polarized light can be used to vary the bandgap of Dirac materials: it opens a gap in graphene and other metallic and semimetallic lattices, or it modifies the magnitude of an existing gap. This will either enhance or reduce a gap, depending on its initial value as well as properties of a host material. Here, we consider gapped dice and Lieb lattices as samples, and we put forward a full theoretical model to reveal how these electronic states are deformed by elliptically-polarized irradiation with a focus on the generation and modification of a bandgap.