Plasmon Dispersions and Polarization in Flat Band Pseudospin-1 Materials with Band Gaps

We investigate the collective electronic properties of pseudospin-1 Dirac-cone materials featuring both flat bands and finite band gaps in their energy spectra. Our study specifically focuses on calculating the dynamical polarization, plasmon dispersions, and their decay rates caused by Landau damping. We also derive analytical expressions for the wave function overlaps in both the gapped dice lattice and the Lieb lattice. The gapped dice lattice, a special case of the more general α-T3 model, retains a symmetric band structure with a nondispersive flat band. In contrast, the Lieb lattice features a flat band located at the bottom of its conduction band. Our findings reveal distinctive characteristics in the plasmon spectra and damping regions for both lattices, which have not been reported in earlier research. Specifically, the particle-hole modes in the Lieb lattice appear as finite regions, while plasmon modes are confined to small wave numbers but extend over a broad frequency range.