Hall quantization and optical conductivity evolution with variable Berry phase in $\alpha$-$T_3$ model

Abstract

The $\alpha$-$T_3$ model is characterized by a variable Berry phase that changes continuously from $\pi$ to $0$. We take advantage of this property to highlight the effects of this underlying geometrical phase on a number of physical quantities. The Hall quantization of the two limiting cases is dramatically different - a relativistic series is associated with a Berry phase of $\pi$ and a non-relativistic series is associated with the other limit. We study the quantization of the Hall plateaux as they continuously evolve from a relativistic to a non-relativistic regime. Additionally, we describe two physical quantities that retain knowledge of the Berry phase, in the absence of a motion-inducing magnetic field. The variable Berry phase of the $\alpha$-$T_3$ model allows us to explicitly describe the Berry phase dependence of the dynamical longitudinal optical conductivity and of the angular scattering probability.

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• Flat Bands and Ferrimagnetic Order in Electronically Correlated Dice-Lattice Ribbons
• Probing Topological signatures in an optically driven $\alpha$-$T_3$ Lattice
• Optical conductivity of semi-Dirac and pseudospin-1 models: Zitterbewegung approach
• Optical response of two-dimensional Dirac materials with a flat band
• Dynamical optical conductivity for gapped $\alpha -{\mathcal{T}}_3$ materials with a curved "flat" band
• Strain-induced pseudo-magnetic field in $\alpha -{\mathcal{T}}_3$ lattice
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• Magnetoplasmons for the $\alpha$-T${}_3$ model with filled Landau levels
• Magnon-magnon interaction and magnon relaxation time in ferromagnetic Cr2Ge2Te6 monolayer
• Enhancement of thermoelectric performance of a nanoribbon made of alpha-${\mathcal{T}}_3$ lattice
• Floquet engineering of topological phase transitions in quantum spin Hall $\alpha$-$T_3$ system
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• Optical properties of two dimensional Dirac Weyl materials with a flatband
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