Dynamical optical conductivity for gapped $\alpha -{\mathcal{T}}_3$ materials with a curved "flat" band

Abstract

We have calculated the dynamical optical conductivity for $\alpha -{\mathcal{T}}_3$ materials in the presence of a finite bandgap in their energy bandstructure. This is a special type of energy dispersions because for all $\alpha -{\mathcal{T}}_3$ materials with a bandgap, except graphene and a dice lattice limits, the flat band receives a non-zero dispersion and assumes a curved shape. The infinite $\mathbf{k}$-degeneracy of the flat energy band is also lifted. Such a low-energy bandstructure could be obtained if an $\alpha -{\mathcal{T}}_3$ material is irradiated off-resonant with circularly polarized light. We have calculated the optical conductivity for the zero and finite temperatures, as well as for the cases of a finite and nearly-zero doping. We have demonstrated that analytical expressions could be in principle obtained for all types of gapped $\alpha -{\mathcal{T}}_3$ materials and provided the closed-form analytical expressions for a gapped dice lattice. Our numerical results reveal some well-known signatures of the optical conductivity in $\alpha -{\mathcal{T}}_3$ and silicene with two non-equivalent bandgaps, as well as demonstrate some very specific features which have not been previously found in any existing Dirac materials.

arXiv comment17 pages, 4 figures

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• Optical properties of two dimensional Dirac Weyl materials with a flatband
• Tuned gap in graphene through laser barrier
• Band structure and optical response of Kekulé-modulated $\alpha -{\mathcal{T}}_3$ model
• Klein tunneling in deformed honeycomb-dice lattice: from massless to massive particles
• Surface states and finite size effects in triple-fold semimetals
• Floquet engineering of spin-valley selective transport in jacutingaite