Frequency-dependent polarizability, plasmons, and screening in the 2D pseudospin-1 dice lattice

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, $\omega_p=q=\mu$, independent of the background dielectric constant. Finally, screening effects are discussed with regard to impurities.