https://doi.org/10.1140/epjb/s10051-023-00596-x
Regular Article - Solid State and Materials
Anatomy of plasmons in generic Luttinger semimetals
1
Department of Physics & Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Tianjin University, 300072, Tianjin, People’s Republic of China
2
Department of Physics, Shiv Nadar Institution of Eminence (SNIoE), Gautam Buddha Nagar, 201314, Ghaziabad, Uttar Pradesh, India
Received:
10
July
2023
Accepted:
12
September
2023
Published online:
11
October
2023
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 (
) 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 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 , 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 
(also known as the inelastic scattering rate) resulting from screened Coulomb interactions. A well-defined sharp peak in the profile of 
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.
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