Polarizability, plasmons and damping in pseudospin-1 gapped materials with a flat band

Abstract

The subject of our present investigation is the collective electronic properties of various types of pseudospin-$1$ Dirac-cone materials with a flat band and finite bandgaps in their low-energy spectra. Specifically, we have calculated the dynamical polarization, plasmon dispersions, as well as their decay rates due to Landau damping and presented the closed-form analytical expressions for the wave function overlaps for both the gapped dice lattice and the Lieb lattice. The gapped dice lattice is a special case of the more general $\alpha$-${\cal T}_3$ model such that its band structure is symmetric and the flat band remains dispersionless. On the other hand, the Lieb lattice has a flat band which appears at the lowest point of its conduction band. Our results for these two materials exhibit unique features in the plasmon spectra and their damping regions, which have never been previously reported. For example, the particle-hole modes of a Lieb lattice appear as finite-size regions, while the plasmon modes exist only in areas with small wave numbers but an extended range of frequencies.