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

TL;DR

This paper investigates the magneto-optical properties of the generalized $oldsymbol{ extalpha - T_3}$ lattice, revealing how Landau levels and conductivities depend on the model's parameters and highlighting the role of flat bands in optical transitions.

Contribution

It introduces a general method to compute Green's functions in the $oldsymbol{ extalpha - T_3}$ model, elucidates Landau level structures, and analyzes magneto-optical conductivities including flat band effects.

Findings

Dominant optical transitions involve flat and propagating bands.

Hall conductivity per valley is non-quantized but sums to an integer.

Landau level structure varies with the $oldsymbol{ extalpha}$ parameter.

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.