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arXiv · 1601.05369

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

E. Illes·J. P. Carbotte·E. J. Nicol
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Abstract

The $α$-$T_3$ model is characterized by a variable Berry phase that changes continuously from $π$ 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 $π$ 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 $α$-$T_3$ 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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E. Illes, J. P. Carbotte, E. J. Nicol. 2016-01-20. Hall quantization and optical conductivity evolution with variable Berry phase in $α$-$T_3$ model. https://doi.org/10.1103/physrevb.92.245410

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