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

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.

19 pages, 8 figures

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Cited by in corpus (9)

• Probing Topological signatures in an optically driven $\alpha$-$T_3$ Lattice
• Dynamical optical conductivity for gapped $\alpha -{\mathcal{T}}_3$ materials with a curved "flat" band
• Optical conductivity of bilayer dice lattices
• Effect of magnetic field on the electronic properties of an $\alpha$-$T_3$ ring
• Orbital magnetization senses the topological phase transition in a spin-orbit coupled $\alpha$-$T_3$ system
• Plasmons in Z2 Topological Insulators
• Influence of Dynamical Floquet Spectrum on the Plasmon Excitations and Exchange Energy of tilted monolayer 1T${}^{\prime }$MoS${}_2$
• Possible realization of hyperbolic plasmons in a few-layered rhenium disulfide
• Interband plasmons due to Mexican hat dispersion in two-dimensional materials with inverted bands