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

TL;DR

This paper provides a theoretical analysis of how off-resonant irradiation affects the electronic states, Berry phases, and symmetries in the $ extit{ extbf{ extit{ extalpha}}}$-$T_3$ lattice, revealing potential for band structure engineering.

Contribution

It introduces a comprehensive theoretical framework for understanding Floquet states and Berry phases in irradiated $ extalpha$-$T_3$ materials, highlighting the influence of polarization and the parameter $ extalpha$.

Findings

Berry phases can be finite even in dice lattices under irradiation.

Electronic properties depend on polarization and valley index.

Irradiation enables band structure engineering in $ extalpha$-$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 $\alpha$-$T_3$ model, to external radiation with various polarizations. Specifically, we have examined the role played by the parameter $\alpha$ 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 $\alpha$ -$T_3$ 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 $\tau$. 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.