materials under external irradiation*

Electron dressed states, or interacting Floquet states, have been derived analytically for α-T₃ materials. These arise from the off-resonant coupling of Dirac pseudospin-1 electrons to the external irradiation. Results will be presented over the allowable range of values of the interaction parameter α 0 < α < 1 and for all possible types of incoming light polarizations. For elliptical and circular polarizations, an energy band gap could be opened, there is no longer symmetry between the valence and conduction bands, and the obtained low-energy bandstructure directly depends on the valley index τ . In contrast, applying linearly polarized light could induce α-dependent anisotropy of the dispersions, but there is no change to the flat band. We have obtained and examined the corresponding wave functions, their structure and Berry phases.