  HgCdTe at a critical cadmium doping has a bulk dispersion which includes two
linear cones meeting at a single point at zero energy, intersecting a nearly
flat band, similar 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. The
calculations show good agreement with recent experimental measurements. We
discuss the signature of the flat band and the split peaks of the
magneto-optics in terms of general pseudospin-s models and propose that the
system exhibits a non-{\pi}-quantized Berry phase, found in recent theoretical
work.
