Landau levels and magneto-optical transport properties of a semi-Dirac system

We study magneto-optical (MO) properties of a semi-Dirac system in presence of a perpendicular magnetic field using kernel polynomial method (KPM) based on the Keldysh formalism in few hundreds of the terahertz (THz) frequency regime. For the semi-Dirac case, the band structure demonstrates a linear (Dirac-like) dispersion along the y direction, while it has a quadratic (nonrelativistic) behavior along the x direction in the Brillouin zone. For comparison, we have also included results for the Dirac systems as well, so that the interplay of the band structure deformation and MO conductivities can be studied. We have found that the MO conductivity shows features in the semi-Dirac system that are quite distinct from the Dirac case in the above mentioned frequency regime. The real parts of the longitudinal MO conductivities, namely Re(sigma(xx)) and Re(sigma(yy)) (which are different in the semi-Dirac case, as opposed to a Dirac one), present a series of resonance peaks as a function of the incident photon energy. We have also found that the absorption peaks corresponding to the y direction are larger (roughly one order of magnitude) than those corresponding to the x direction for the semi-Dirac case. In the case of the MO Hall conductivity, that is, Re(sigma(xy)), there are extra peaks in the spectra compared to the Dirac case, which originate from the distinct optical transitions of the carriers from one Landau level to another. These peaks are otherwise absent in a Dirac system, where some of these peaks result from transitions between pairs of Landau levels that differ by the same energy and hence those peaks can not be resolved. We have also explored how the carrier concentration influences the MO conductivities. In the semi-Dirac case, there is the emergence of additional peaks yet again in the absorption spectrum underscoring the presence of an asymmetric dispersion compared to the Dirac case. Further, we have explored the interplay between the polarization of the incident beam and the features of the absorption spectra, which can be probed in experiments. Finally, we evaluate the MO activity of the medium by computing the Faraday rotation angle theta(F). The semi-Dirac case shows two maxima and two minima of theta(F) at different photon energies, which can be captured in experiments.