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arXiv · 1605.09588

Frequency dependent magneto-optical conductivity in the generalized $\alpha - T_3$ model

Áron Dániel Kovács·Gyula Dávid·Balázs Dóra·József Cserti
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Abstract

We have studied a generalized three band crossing model in 2D, the generalized $\alpha - T_3$ lattice, ranging from the pseudospin-1 Dirac equation through a quadratic+flat band touching to the pseudospin-1/2 Dirac equation. A general method is presented to determine the operator form of the Green's function, being gauge and representation independent. This yields the Landau level structure in a quantizing magnetic field and the longitudinal and transversal magneto-optical conductivities of the underlying system Although the magneto-optical selection rules allow for many transitions between Landau levels, the dominant one stems from exciting a particle from/to the flat band to/from a propagating band. The Hall conductivity from each valley is rational (not quantized at all), in agreement with Berry phase considerations, though their sum is always integer quantized.

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Áron Dániel Kovács, Gyula Dávid, Balázs Dóra, József Cserti. 2016-05-31. Frequency dependent magneto-optical conductivity in the generalized $\alpha - T_3$ model. https://doi.org/10.1103/physrevb.95.035414

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