Finite-temperature plasmons, damping, and collective behavior in the ?-T-3 model

We have conducted a thorough theoretical and numerical investigation of the electronic susceptibility, the polarizability, the plasmon modes and their damping rates, and the static screening in pseudospin-1 Dirac-cone materials with a flat band, or in a general alpha - T3 model, at finite temperatures. This study includes calculating the polarization function and the plasmon dispersions and their damping rates at arbitrary temperatures and obtaining analytical approximations in the long-wavelength limit at low and high temperatures. We further demonstrate that the integral transformation of the polarization function cannot be used directly for a dice lattice, revealing some fundamental properties and important applicability limits of the flat-band dispersion model. As kBT/EF << 1, the dominant temperature-dependent change of the polarization function and plasmon modes comes from the mismatch between finite-temperature chemical potential and zero-temperature Fermi energy. In particular, we have obtained several closed-form semianalytical expressions for the static-limit polarization function of an arbitrary alpha - T3 material and acquired exact analytical formulas in all limits of high, low, and zero temperature. This result is of tremendous importance for all types of transport and screening studies of the flat-band Dirac materials.