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

Abstract

We study magneto-optical (MO) properties of a semi-Dirac nanoribbon in presence 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 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 near the ultra-violet and the visible regimes. The real parts of the longitudinal 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 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. 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, $\theta_{F}$.