We calculate the dynamic polarizability under the random phase approximation for the dice lattice. This two-dimensional system gives rise to massless Dirac fermions with pseudospin-1 in the low-energy quantum excitation spectrum, providing a Dirac-cone plus flat-band dispersion. Due to the presence of the flat band, the polarizability shows key differences to that of graphene (the pseudospin-1/2 Dirac material). We find that the plasmon branch is pinched in to a single point, ωp = q = µ, independent of the background dielectric constant. Finally, screening effects are discussed with regard to impurities.

Hg 1−x CdxTe 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.

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The popularity of graphene-a pseudospin-1 2 two-dimensional Dirac-Weyl material-has prompted the search for related materials and the characterization of their properties. In this work, the magneto-optical conductivity is calculated for systems that obey the general pseudospin-s two-dimensional Dirac-Weyl Hamiltonian, with particular focus on s = { 1 2 ,1, 3 2 ,2}. This generalizes calculations that have been made for s = 1 2 and follows previous work on the optical response of these systems in zero field. In the presence of a magnetic field, Landau levels condense out of the 2s + 1 energy bands. As the chemical potential in a system is shifted, patterns arise in the appearance and disappearance of certain peaks within the optical spectra. These patterns are markedly different for each case considered, creating unique signatures in the magneto-optics. The general structure of each spectrum and how they compare is discussed.