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We study magneto-optical (MO) properties of a semi-Dirac nanoribbon inpresence of a perpendicular magnetic field using Kernel Polynomial Method (KPM)based on the Keldysh formalism in the experimental (terahertz frequency)regime. For comparison, we have also included results for the Dirac systems aswell, so that the interplay of the band structure deformation and MOconductivities can be studied. We have found that the MO conductivity showsfeatures in the semi-Dirac system that are quite distinct from the Dirac casenear the ultra-violet and the visible regimes. The real parts of thelongitudinal conductivities, namely Re($\sigma_{xx}$) and Re($\sigma_{yy}$)(which are different in the semi-Dirac case, as opposed to a Dirac one) presenta series of resonance peaks as a function of the incident photon energy. Wehave also found that the absorption peaks corresponding to the $y$-directionare larger (roughly one order of magnitude) than those corresponding to the$x$-direction for the semi-Dirac case. In the case of the Hall conductivity,that is, Re($\sigma_{xy}$), there are extra peaks in the spectra compared tothe Dirac case which originate from the distinct optical transitions of thecarriers from one Landau level to another. We have also explored how thecarrier concentration influences the MO conductivities. In the semi-Dirac case,there is the emergence of additional peaks yet again in the absorption spectrumunderscoring the presence of an asymmetric dispersion compared to the Diraccase. Further, we have explored the interplay between the polarization of theincident beam and the features of the absorption spectra which can be probed inexperiments. Finally, we evaluate the MO activity of the medium by computingthe Faraday rotation angle, $\theta_{F}$.

Magneto-optical properties of a semi-Dirac nanoribbon in the terahertz frequency regime