Anatomy of plasmons in generic Luttinger semimetals

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.