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 (or density) decays as r −2 and r −3in two, and three dimensions respectively, and as r −1 for one dimensional non-interacting systems. 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 electrons in different experimental systems with varying dimensionality.

We study the linear response of doped three dimensional Dirac and Weyl semimetals to vector potentials, by calculating the wave-vector and frequency dependent current-current response function analytically. The longitudinal part of the dynamic current-current response function is then used to study the plasmon dispersion, and the optical conductivity. The transverse response in the static limit yields the orbital magnetic susceptibility. In a Weyl semimetal, along with the current-current response function, all these quantities are significantly impacted by the presence of parallel electric and magnetic fields (a finite E · B term), and can be used to experimentally explore the chiral anomaly.

In this article, we explore the anisotropic electron energy loss spectrum (EELS) in monolayer phosphorene based on ab-initio time dependent density functional theory calculations. Similar to black phosphorous, the EELS of undoped monolayer phosphorene is characterized by anisotropic excitonic peaks for energies in vicinity of the bandgap, and by interband plasmon peaks for higher energies. On doping, an additional intraband plasmon peak also appears for energies within the bandgap. Similar to other two dimensional systems, the intraband plasmon peak disperses as ω pl ∝ √ q in both the zigzag and armchair directions in the long wavelength limit, and deviates for larger wavevectors. The anisotropy of the long wavelength plasmon intraband dispersion is found to be inversely proportional to the square root of the ratio of the effective masses: ω pl (qŷ)/ω pl (qx) = mx/my.

We explore the collective density oscillations of a collection of charged massive Dirac particles, in one, two and three dimensions and their one dimensional superlattice. We calculate the long wavelength limit of the dynamical polarization function analytically, and use the random phase approximation to obtain the plasmon dispersion. The density dependence of the long wavelength plasmon frequency in massive Dirac systems is found to be different as compared to systems with parabolic, and gapless Dirac dispersion. We also calculate the long wavelength plasmon dispersion of a 1d metamaterial made from 1d and 2d massive Dirac plasma. Our analytical results will be useful for exploring the use of massive Dirac materials as electrostatically tunable plasmonic metamaterials and can be experimentally verified by infrared spectroscopy as in the case of graphene [Nat. Nanotechnol. 6, 630 (2011)].

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