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...

The dressed states arising from the interaction between electrons and holes, and off-resonant electromagnetic radiation have been investigated for recently fabricated gapped and anisotropic black phosphorus. Our calculations were carried out for the low-energy electronic subbands near the Γ point. States for both linear and circular polarizations of the incoming radiation have been computed. However, our principal emphasis is on linearly polarized light with arbitrary polarization since this case has not been given much attention for dressing fields imposed on anisotropic structures. We have considered various cases for one-and few-layer phosphorus, including massless Dirac fermions with tunable in-plane anisotropy. Initial Hamiltonian parameters are renormalized in a largely different way compared to those for previously reported for gapped Dirac structures and, most importantly, existing anisotropy which could be modified in every direction.

We calculate the energy bands for graphene monolayers when electrons move through a periodic electrostatic potential in the presence of a uniform perpendicular magnetic field. We clearly demonstrate the quantum fractal nature of the energy bands at reasonably low magnetic fields. We present results for the energy bands as functions of both wave number and magnetic flux through the unit cells of the resulting moiré superlattice. The effects due to pseudospin coupling and Landau orbit mixing by a strong scattering potential have been exhibited. At low magnetic fields when the Landau orbits are much larger than the period of the modulation, the Landau levels are only slightly broadened. This feature is also observed at extremely high magnetic fields. The density of states has been calculated and shows a remarkable self-similarity like the energy bands. We estimate that for modulation period of 10 nm the region where the Hofstadter butterfly is revealed is B 2 T.