Magnetic properties of the $\alpha$-$T_3$ model: magneto-optical conductivity and the Hofstadter butterfly

TL;DR

This paper investigates the magnetic properties of the $ extalpha$-$T_3$ model, focusing on magneto-optical conductivity and Hofstadter butterfly spectra, revealing hybrid system signatures and spectral periodicity changes.

Contribution

It provides the first detailed analysis of magnetic responses in the $ extalpha$-$T_3$ model, bridging graphene and dice lattice behaviors.

Findings

Doublet structure in magneto-optical peaks due to Landau level differences

Evolution of Hofstadter butterfly with periodicity changing by a factor of three

Distinct signatures of hybrid pseudospin system in magnetic spectra

Abstract

The $\alpha$-$T_3$ model extrapolates between the pseudospin $S=1/2$ honeycomb lattice of graphene and the pseudospin $S=1$ dice lattice via parameter $\alpha$. We present calculations of the magnetic properties of this hybrid pseudospin model, namely the absorptive magneto-optical conductivity and the Hofstadter butterfly spectra. In the magneto-optics curves, signatures of the hybrid system corollary a doublet structure present in the peaks, resulting from differing Landau level energies in the $K$ and $K^{\prime}$ valleys. In the Hofstadter spectra, we detail the evolution of the Hofstadter butterfly as it changes its periodicity by a factor of three as we vary between the two limiting cases of the $\alpha$-$T_3$ model.