  We consider theoretically as a function of temperature the plasmon mode
arising in three-dimensional Dirac liquids, i.e., systems with linear chiral
relativistic single-particle dispersion, within the random phase approximation.
We find that whereas no plasmon mode exists in the intrinsic (undoped) system
at zero temperature, there is a well-defined finite-temperature plasmon with
superlinear temperature dependence, rendering the plasmon dispersion widely
tunable with temperature. The plasmon dispersion contains a logarithmic
correction due to the ultraviolet-logarithmic renormalization of the electron
charge, manifesting a fundamental many-body interaction effect as in quantum
electrodynamics. The plasmon dispersion of the extrinsic (doped) system
displays a minimum at finite temperature before it crosses over to the
superlinear intrinsic behavior at higher temperature, implying that the
high-temperature plasmon is a universal feature of Dirac liquids irrespective
of doping. This striking characteristic temperature dependence of intrinsic
Dirac plasmons along with the logarithmic renormalization is a unique
manifestation of the three-dimensional relativistic Dirac nature of
quasiparticle excitations and serves as an experimentally observable signature
of three-dimensional Dirac materials.
