[Paper Review] Dynamical polarization, plasmon model, and the Friedel oscillation of the screened potential in doped Dirac and Weyl system

Chen-Huan Wu|arXiv (Cornell University)|Sep 1, 2018

Topological Materials and Phenomena9 references4 citations

TL;DR

This paper investigates dynamical polarization, plasmon dispersion, and Friedel oscillations in doped gapped two-dimensional Dirac and three-dimensional Weyl systems using a low-energy tight-binding model. It reveals that chiral symmetry suppresses backscattering at q=2kF, leading to a faster r⁻⁴ decay of the screened potential in Weyl systems—distinct from the r⁻² or r⁻³ decay in conventional systems—due to enhanced screening and topological effects.

ABSTRACT

We discuss the dynamical polarization, plasmon dispersion, relaxation time, and the Friedel oscillation of screened potential of the two-dimension Dirac and three-dimension Weyl system (which are gapped) in the low-energy tigh-binding model. The results, like the Fermi wavevector, Thomas-Fermi wavevector, and longitudinal conductivity are obtained in different dimensions. Some important conclusions are detailedly discussed in this paper, including the screening character under short or long range Coulomb interaction, and the longitudinal conductivity in two- or three-dimensions. The longitudinal conductivity in optical limit is distinguishing for the case of two-dimension system and three-dimension system. The density-dependence (including the carrier density and the impurity concentration) of the Fermi wavevector, dc conductivity, and the relaxation time are discussed. Specially, for the doped Weyl system, the pumped carrier density due to the chiral anomaly origin from electromagnetic response is controlled by the internode relaxation time which has also been analyzed. %The model for which the calculations based on is the low-energy tight-binding model as presented in the Sec.2, %i.e., the results in this paper is for the low-temperature and low-energy case %and it's thus possible to carrying out a logarithmic self-energy correction to the relaxation time as we discussed in the text. %The difference between the longitudinal conductivity in serversal systems is also been discussed. Our results is helpful to the application of the Dirac or Weyl systems as well as the study on their low-temperature characters.

Motivation & Objective

• To understand the dynamical polarization and screening properties of doped gapped Dirac and Weyl systems at low energies.
• To investigate how chiral symmetry and topological effects influence plasmon dispersion and relaxation time.
• To compare the Friedel oscillation behavior of the screened potential in 2D Dirac systems (e.g., silicene) versus 3D Weyl semimetals.
• To analyze the role of carrier density, impurity concentration, and internode relaxation time in determining transport and screening characteristics.
• To clarify the distinction between short-range and long-range Coulomb interactions in determining screening decay behavior.

Proposed method

• Uses a low-energy tight-binding model to describe the electronic structure of gapped 2D Dirac and 3D Weyl systems.
• Calculates the dynamical polarization function Π(q,ω) to determine screening effects and plasmon dispersion relations.
• Evaluates the static polarization and its derivative to identify kinks at q=2kF, indicating backscattering suppression.
• Derives the screened potential using the Thomas-Fermi approximation and Friedel oscillation contributions.
• Applies effective dielectric constants ε* to account for environment screening, including contributions from interband transitions.
• Analyzes the relaxation time τ and transport time, particularly in relation to internode scattering and impurity concentration.

Experimental results

Research questions

• RQ1 How does chiral symmetry in Dirac and Weyl systems affect the backscattering at q=2kF and the resulting Friedel oscillation decay?
• RQ2 What is the functional form of the screened potential due to charged impurities in 2D Dirac and 3D Weyl systems under different interaction ranges?
• RQ3 How does the internode relaxation time in Weyl semimetals influence the pumped carrier density and transport properties?
• RQ4 What are the differences in longitudinal conductivity and plasmon dispersion between 2D Dirac and 3D Weyl systems in the optical limit?
• RQ5 How do carrier density and impurity concentration affect the Fermi wavevector, Thomas-Fermi wavevector, and dc conductivity?

Key findings

• The screened potential in 3D Weyl semimetals decays as ∼sin(2kFr)/r⁴ due to chiral anomaly-induced suppression of backscattering at q=2kF.
• In contrast, 2D Dirac systems (e.g., silicene) and 2DEG exhibit slower r⁻² or r⁻³ decay, depending on the system and interaction range.
• The static polarization function dΠ/dq shows a discontinuous second derivative at q=2kF in gapped Weyl systems, similar to gapped Dirac systems.
• For 3D Weyl semimetals, the Friedel oscillation contribution to the screened potential scales as ∼sin(2kFr)/r⁴, while for 2DEG it scales as ∼sin(2kFr)/r².
• The internode relaxation time in Weyl semimetals (e.g., Eu₂Ir₂O₇) is estimated at ~25 fs, significantly longer than in silicene (~18.2 ps), indicating slower charge relaxation.
• The effective dielectric constant ε* is enhanced in 2D Dirac systems due to interband contributions, while it reduces to ε*=1 in bilayer systems due to suppressed Π⁻(q,ω).