Calculation of the magneto-optical response of Kane fermions in HgCdTe

The concentration $x=x_{c}\approx 0.17$ in ${\rm Hg}_{x}{\rm Cd}_{1-x}{\rm Te}$ describes a critical value in the phase transition between semimetal ($xx_{c}$). At this critical value, the low-energy quasiparticle dispersion exhibits a node at the intersection of two doubly degenerate linear cones and an equally degenerate flat band; quasiparticles that have been dubbed Kane fermions [1]. We present our results for the calculation of the magneto-optical spectra of these Kane fermions in the three-dimensional material, which can be compared to experiment, and also for those confined to only two-dimensions. The latter allows for a direct comparison to the analogous theoretical Dirac-Weyl system in two dimensions with pseudospin one [2]. \newline \newline [1] M. Orlita \textit{et al}. \textit{Nature Phys}. \textbf{10}, 233 (2014). \newline [2] J.D. Malcolm and E.J. Nicol. \textit{Phys. Rev. B} \textbf{90}, 035405 (2014).