Collective modes in multi-Weyl semimetals

TL;DR

This paper analytically studies collective plasma modes in 3D multi-Weyl semimetals with anisotropic and isotropic dispersions, revealing how band structure and chirality influence plasmon damping and frequency shifts.

Contribution

It provides a comprehensive analytical analysis of plasma frequencies and damping in multi-Weyl semimetals with arbitrary band dispersions, highlighting the effects of anisotropy and chirality.

Findings

Interband transitions and chirality cause depolarization shifts in plasma frequencies.

Plasmons in quadratic dispersions are undamped at all densities.

Higher-order dispersions exhibit damping below a critical density.

Abstract

We investigate collective modes in three dimensional (3D) gapless multi-Weyl semimetals with anisotropic energy band dispersions (i.e., $E\sim \sqrt{ k_{\parallel}^{2J} + k_z^2}$, where $k_{\parallel}$ and $k_z$ are wave vectors and $J$ is a positive integer). For comparison, we also consider the gapless semimetals with the isotropic band dispersions (i.e., $E\sim k^J$). We calculate analytically long-wavelength plasma frequencies incorporating interband transitions and chiral properties of carriers. For both the isotropic and anisotropic cases, we find that interband transitions and chirality lead to the depolarization shift of plasma frequencies. For the isotropic parabolic band dispersion (i.e., $N=2$, $E\sim k^2$), the long-wavelength plasma frequencies lie outside the single particle excitation regions for all carrier densities, and thus the plasmons do not decay via Landau damping. For the higher-order band dispersions ($N \ge 3$) the long-wavelength plasmons experience damping below a critical density. For systems with the anisotropic dispersion the density dependence of the long-wavelength plasma frequency along the direction of non-linear dispersion behaves like that of the isotropic linear band model ($N=1$), while along the direction of linear dispersion it behaves like that of the isotropic non-linear model ($N \ge 2$). Plasmons along both directions remain undamped over a broad range of densities due to the chirality induced depolarization shift. Our results provide a comprehensive picture of how band dispersion and chirality affect plasmon behaviors in 3D gapless chiral systems with the arbitrary band dispersion.