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

TL;DR

This paper provides analytical expressions for the dynamical polarization function of massive and massless Dirac particles in one, two, and three dimensions, elucidating their screening and plasmon dispersion properties.

Contribution

It offers new analytical formulas for the polarization function and insights into screening and plasmon behavior across different dimensions for Dirac systems.

Findings

Screened potential decays as r^{-1}, r^{-2}, r^{-3} in 1D, 2D, 3D for massive Dirac systems.

Massless Dirac systems lack screening and Friedel oscillations in 1D.

Decay of screened potential in massless systems is r^{-3} and r^{-4} in 2D and 3D.

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.