Optical conductivity of gapped -T3 materials with a deformed flat band

We derive and discuss the optical conductivity of alpha-T3 materials with a finite band gap in their energy dispersions. In contrast with familiar alpha-T3 materials, this constitutes a nontrivial case since the flat band changes into a curved one and two other branch dispersion relations become nonlinear beyond the limiting cases for graphene and the dice lattice. Such a unique band structure appears if the alpha-T3 material is irradiated by a circularly polarized light nonresonantly. For this system, we have obtained optical conductivities at either zero or finite temperatures with nonzero or near-zero doping. Additionally, we demonstrate that analytical expressions can be obtained for all types of gapped alpha-T3 materials, and, meanwhile, provide closed-form analytical expressions for a gapped dice lattice. Our current paper reproduces known properties of optical conductivity in unirradiated alpha-T3 materials and silicene with two nonequivalent band gaps and, furthermore, demonstrates some very interesting irradiation-enabled behaviors which are absent in any Dirac materials. The discovery of unusual properties for the optical conductivity of gapped alpha-T3 in this paper is expected to have many promising device applications, such as photodetectors, optical modulators, and metasurfaces.