Kavli Affiliate: Jing Wang

| Authors: Jing Wang, Ipsita Mandal

| Summary:

We investigate the parameter regimes favourable for the emergence of plasmons

in isotropic, anisotropic, and band-mass 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

degenrate. 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 parameter $X$, to numerically compute the quasiparticle

damping rate $tau$ resulting from screened Coulomb interactions. A

well-defined sharp peak in the profile of the inelastic scattering rate

$tau^{-1}$ 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.