Optical conductivity of gapped <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mtext>−</mml:mtext><mml:msub><mml:mi mathvariant="script">T</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> materials with a deformed flat band

Abstract

We derive and discuss the optical conductivity of $\ensuremath{\alpha}\ensuremath{-}{\mathcal{T}}_{3}$ materials with a finite band gap in their energy dispersions. In contrast with familiar $\ensuremath{\alpha}\ensuremath{-}{\mathcal{T}}_{3}$ 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 $\ensuremath{\alpha}\ensuremath{-}{\mathcal{T}}_{3}$ 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 $\ensuremath{\alpha}\ensuremath{-}{\mathcal{T}}_{3}$ materials, and, meanwhile, provide closed-form analytical expressions for a gapped dice lattice. Our current paper reproduces known properties of optical conductivity in unirradiated $\ensuremath{\alpha}\ensuremath{-}{\mathcal{T}}_{3}$ 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 $\ensuremath{\alpha}\ensuremath{-}{\mathcal{T}}_{3}$ in this paper is expected to have many promising device applications, such as photodetectors, optical modulators, and metasurfaces.

Topics & Concepts