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.

• Received 25 January 2016
• Revised 11 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.165433