Anatomy of plasmons in generic Luttinger semimetals

Kavli Affiliate: Jing Wang

| First 5 Authors: Jing Wang, Ipsita Mandal, , ,

| Summary:

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 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.

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