Anatomy of plasmons in generic Luttinger semimetals

TL;DR

This paper explores the conditions under which plasmons can emerge in Luttinger semimetals, emphasizing the roles of temperature, doping, and material parameters, and finds that the parameter X significantly influences plasmon formation.

Contribution

It provides a detailed analysis of plasmon emergence in Luttinger semimetals considering various parameters, highlighting the importance of the variable X in tuning plasmonic behavior.

Findings

Higher values of X promote plasmon emergence.

Plasmon features are insensitive to anisotropy and mass asymmetry.

Finite temperature or doping is necessary for plasmons to exist.

Abstract

We investigate the parameter regimes favourable for the emergence of plasmons in isotropic, anisotropic, and band-mass symmetric and asymmetric Luttinger semimetals (LSMs). An LSM harbours a quadratic band-crossing point (QBCP) in its bandstructure, where the upper and lower branches of dispersion are doubly degenerate. While a nonzero temperature ($T$) can excite particle-hole pairs about the Fermi level due to thermal effects (even at zero doping), a finite doping ($\mu$) sets the Fermi level away from the QBCP at any $T$, leading to a finite Fermi surface (rather than a Fermi point). Both these conditions naturally give rise to a finite density of states. A nonzero value of $T$ or $\mu$ is thus a necessary condition for a plasmon to exist, as otherwise the zero density of states at the QBCP can never lead to the appearance of this collective mode. In addition to $T$ and $\mu$, we consider the effects of all possible parameters like cubic anisotropy, band-mass asymmetry, and a material-dependent variable $X$ that is proportional to the mass (of the quasiparticle) and the number of fermion flavours. We implement a random-phase-approximation to compute the quasiparticle decay rate $ \tau^{-1} $ (also known as the inelastic scattering rate) resulting from screened Coulomb interactions. A well-defined sharp peak in the profile of $\tau^{-1}$ signals the appearance of a plasmon. From our results, we conclude that $X$ turns out to be a crucial tuning parameter, as higher values of $X$ assist in the emergence of plasmons. On the other hand, the features are broadly insensitive to cubic anisotropy and band-mass asymmetry.