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-T3 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 -T3 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 lowenergy 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.

We investigated the Dirac electrons transmission through a potential barrier in the presence of circularly polarized light. An anomalous photon-assisted enhanced transmission is predicted and explained in a comparison with the well-known Klein paradox. It is demonstrated that the perfect transmission for nearly-head-on collision in an infinite graphene is suppressed in gapped dressed states of electrons, which is further accompanied by shift of peaks as a function of the incident angle away from the head-on collision. In addition, the perfect transmission in the absence of potential barrier is partially suppressed by a photon-induced gap in illuminated graphene. After the effect of rough edges of the potential barrier or impurity scattering is included, the perfect transmission with no potential barrier becomes completely suppressed and the energy range for the photon-assisted perfect transmission is reduced at the same time.

In the presence of external off-resonance and circularly-polarized irradiation, we have derived a many-body formalism and performed a detailed numerical analysis for both the conduction and optical currents in α − T3 lattices. The calculated complex many-body dielectric function, as well as conductivities of displacement and transport currents, display strong dependence on the latticestructure parameter α, especially approaching the graphene limit with α → 0. Unique features in dispersion and damping of plasmon modes are observed with different α values, which are further accompanied by a reduced transport conductivity under irradiation. The discovery in this paper can be used for designing novel multi-functional nanoelectronic and nanoplasmonic devices. I. INTRODUCTIONSo far, the α − T 3 model seems to present prospective opportunities for revolutionizing low-dimensional physics through novel two-dimensional (2D) materials. 1 Its atomic configuration consists of a graphene-type honeycomb lattice along with an additional site, i.e., a hub atom at the center of each hexagon. 2 An essential structure parameter α = tan φ, which enters into the low-energy Dirac-Weyl pseudospin-1 Hamiltonian for α − T 3 model, is found to be the ratio between the rim-to-hub and rim-to-rim hopping coefficients. This parameter affects all fundamental electronic properties of the α − T 3 lattice through topological characteristics embedded in its pseudospin-1 wave functions. Parameter α can vary from 0 to 1, corresponding to different types of α − T 3 materials, and the control of it could lead to some important technological applications for electronic and optoelectronic devices. Here, the case with α = 0 relates to graphene with a completely separated flat band, whereas α = 1 results in a pseudospin-1 dice lattice which has been fabricated and studied considerably. 3,4 Consequently, the α − T 3 model may be viewed as an interpolation between graphene and the dice lattice (or pseudospin-1 T 3 model). Its low-energy dispersion consists of a Dirac cone, similar to that for graphene, 5 as well as a flat band with zero-energy separating the valence from the conduction band for these pseudospin-1 materials. 6,7 In recent years, there have been numerous attempts for experimental realization of the α − T 3 model. Its topological characteristics, i.e., a Dirac cone with three bands touching at a single point, was observed in the triplon band structure of SrCu 2 (BO 3 ) 2 , as an example of general Mott-Hubbard insulators. 8 Moreover, dielectric photonic crystals with zero refractive index also display Dirac cone dispersion at the center of the Brillouin zone under an accidental degeneracy. 9,10 Most importantly, there exist various types of photonic Lieb lattices, 11,12 consisting of a 2D array of optical waveguides. Such waveguide-lattice structure is shown to have a three-band structure, including a perfectly flat middle band.Further to a relatively recent proposal on α − T 3 model, there have been a lot of crucial publications devoted to inv...