Anisotropic density fluctuations, plasmons, and Friedel oscillations in nodal line semimetal

TL;DR

This paper investigates the anisotropic density fluctuations, plasmons, and Friedel oscillations in nodal line semimetals, revealing unique angle-dependent features and singularities in their polarizability in both static and dynamic regimes.

Contribution

It provides a detailed analysis of the static and dynamic polarizability of doped and undoped nodal line semimetals, highlighting their anisotropic responses and plasmon behaviors, which were previously unexplored.

Findings

Highly anisotropic Friedel oscillations with angle-dependent power law

Two singular lines in dynamical polarizability at specific energy-momentum relations

Anisotropic plasmon dispersion and angle-dependent plasma frequencies

Abstract

Motivated by recent experimental efforts on three-dimensional semimetals, we investigate the static and dynamic density response of the nodal line semimetal by computing the polarizability for both undoped and doped cases. The nodal line semimetal in the absence of doping is characterized by a ring-shape zero energy contour in momentum space, which may be considered as a collection of Dirac points. In the doped case, the Fermi surface has a torus shape and two independent processes of the momentum transfer contribute to the singular features of the polarizability even though we only have a single Fermi surface. In the static limit, there exist two independent singularities in the second derivative of the static polarizability. This results in the highly anisotropic Friedel oscillations which show the angle-dependent algebraic power law and the beat phenomena in the oscillatory electron density near a charged impurity. Furthermore, the dynamical polarizability has two singular lines along $\hbar\omega = \gamma p$ and $\hbar\omega = \gamma p \sin\eta$, where $\eta$ is the angle between the external momentum $\vec{p}$ and the plane where the nodal ring lies. From the dynamical polarizability, we obtain the plasmon modes in the doped case, which show anisotropic dispersions and angle-dependent plasma frequencies. Qualitative differences between the low and high doping regimes are discussed in light of future experiments.