Magneto-optics of massless Kane fermions: Role of the flat band and unusual Berry phase

Hg_1-xCdₓTe at a critical doping x=xc≈0.17 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. These 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-π-quantized Berry phase, found in recent theoretical work.