Dynamical polarizability, screening, and plasmons in one, two, and three dimensional massive Dirac systems

Abstract

We study the density-density response function of a collection of charged massive Dirac particles and present analytical expressions for the dynamical polarization function in one, two and three dimensions. The polarization function is then used to find the dispersion of the plasmon modes, and electrostatic screening of Coulomb interactions within the random phase approximation. We find that for massive Dirac systems, the oscillating screened potential decays as $r^{-1}$, $r^{-2}$ and $r^{-3}$ in one, two, and three dimensions respectively. However for massless Dirac systems there is no electrostatic screening or Friedel oscillation in one dimension, and the oscillating screened potential decays as $r^{-3}$ and $r^{-4}$, in two and three dimensions respectively. Our analytical results for the polarization function will be useful for exploring the physics of massive and massless Dirac materials in different experimental systems with varying dimensionality.

12 pages and 4 figures; revised version with several corrections

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Cited by in corpus (22)

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• Integrated Plasmonics: Broadband Dirac Plasmons in Borophene
• Determining Dark Matter-Electron Scattering Rates from the Dielectric Function
• Dirac Materials for Sub-MeV Dark Matter Detection: New Targets and Improved Formalism
• Anisotropic plasmons, Friedel oscillations and dynamical screening in $8-Pmmn$ borophene
• A novel undamped gapless plasmon mode in tilted type-II Dirac semimetal
• Dynamic current-current susceptibility in 3D Dirac and Weyl semimetals
• Intrinsic first and higher-order topological superconductivity in a doped topological insulator
• Influence of Landau levels in the phonon dispersion of Weyl semimetals
• Dielectric and electronic properties of three-dimensional Luttinger semimetals with a quadratic band touching
• Plasmons in topological insulator cylindrical nanowires
• Plasmon Fizeau drag in 3D Dirac and Weyl semimetals
• Intrinsic nonreciprocal bulk plasmons in noncentrosymmetric magnetic systems
• Dynamical polarization, optical conductivity and plasmon mode of a linear triple component fermionic system
• Theory of Friedel oscillations in monolayer graphene and group-VI dichalcogenides in a magnetic field
• Acoustic plasmons in type-I Weyl semimetals
• Dynamical spin-spin susceptibility of Silicene
• Layered Topological Antiferromagnetic Metal at Room Temperature -- YbMn${}_2$Ge${}_2$
• Collective plasmonic modes in the chiral multifold fermionic material CoSi
• Dynamical density response and collective modes of topological insulator ultra-thin films
• Unveiling Novel Resonant Interband Contribution to Polarizability in three-dimensional systems
• Anomalous screening in narrow-gap carbon nanotubes