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

TL;DR

This paper calculates the dynamical optical conductivity of gapped $ ext{alpha-} ext{T}_3$ materials with curved flat bands, revealing unique optical signatures and providing analytical formulas for various conditions.

Contribution

It introduces analytical expressions for the optical conductivity of gapped $ ext{alpha-} ext{T}_3$ materials with curved flat bands, including the gapped dice lattice, and explores their optical signatures.

Findings

Analytical formulas for optical conductivity across different gapped $ ext{alpha-} ext{T}_3$ materials.

Identification of unique optical features not seen in other Dirac materials.

Demonstration of effects of finite temperature and doping on optical responses.

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 ${\bf k}$-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.