Frequency-dependent magneto-optics and the role of the flat band for massless Kane fermions
HgCdTe at a critical cadmium doping exhibits a bulk dispersion which includes two linear cones meeting at a single point at zero energy, intersecting a nearly flat band, similar in dispersion to the pseudospin-1 Dirac-Weyl system. In the presence of a finite magnetic field, these bands condense into highly degenerate Landau levels. We have numerically calculated the frequency-dependent magneto-optical and zero-field conductivity of this material using the Kane model in the Kubo formula. Found in this spectrum is a signature of the flat band. These calculations are compared to recent experimental measurements, showing good agreement [M. Orlita et al., Nat. Phys. 10, 233 (2014)]. Discussions are also made in broader comparisons to the Dirac-Weyl system.