Finite-temperature plasmons, damping and collective behavior for $\alpha-\mathcal{T}_3$ model

TL;DR

This paper provides a comprehensive theoretical and numerical analysis of plasmons, damping, and screening in $oldsymbol{ ext{alpha-}oldsymbol{ ext{T}_3}}$ materials at finite temperatures, revealing fundamental properties and analytical formulas for these phenomena.

Contribution

It introduces new analytical expressions for the polarization function and plasmon behavior in $oldsymbol{ ext{alpha-}oldsymbol{ ext{T}_3}}$ models, highlighting limits of existing transformation methods.

Findings

Analytical formulas for polarization at various temperatures.

Identification of limits for integral transformation applicability.

Temperature effects on plasmon dispersion and damping rates.

Abstract

We have conducted a thorough theoretical and numerical investigation of the electronic susceptibility, polarizability, plasmons, their damping rates, as well as the static screening in pseudospin-1 Dirac cone materials with a flat band, or for a general $\alpha - \mathcal{T}_3$ model, at finite temperatures. This includes calculating the polarization function, plasmon dispersions and their damping rates at arbitrary temperatures and obtaining analytical approximations the long wavelength limit, low and high temperatures. We 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 dispersions model. At $k_B T \ll E_F$, the largest temperature-induced change of the polarization function and plasmons comes from the mismatch between the chemical potential and the Fermi energy. We have also obtained a series of closed-form semi-analytical expressions for the static limit of the polarization function of an arbitrary $\alpha - \mathcal{T}_3$ material at any temperature with exact analytical formulas for the high, low and zero temperature limits which is of tremendous importance for all types of transport and screening calculations for the flat band Dirac materials.