Peculiar electronic states, symmetries and Berry phases in irradiated $α$-$T_3$ materials

Abstract

We have laid out the results of a rigorous theoretical investigation into the response of electron dressed states, i.e., interacting Floquet states arising from the off-resonant coupling of Dirac spin-1 electrons in the $α$-$T_3$ model, to external radiation with various polarizations. Specifically, we have examined the role played by the parameter $α$ that is a measure of the coupling strength with the additional atom at the center of the honeycomb graphene lattice and which, when varied, continuously gives a different Berry phase. We have found that the electronic properties of the $α$ -$T_3$ model (consisting of a flat band and two cones) could be modified depending on the polarization of the imposed irradiation. We have demonstrated that under elliptically-polarized light the low-energy band structure of such lattice directly depends on the valley index $τ$. We have obtained and analyzed the corresponding wave functions, their symmetries and the corresponding Berry phases, and revealed that such phases could be finite even for a dice lattice, which has not been observed in the absence of the dressing field. This results lead to possible radiation-generated band structure engineering, as well as experimental and technological realization of such optoelectronic devices and photonic crystals.