Universality of plasmon excitations in Dirac semimetals

The recent experimental discovery of ${\rm Cd_3 As_2}$ and ${\rm Na_3 Bi}$ Dirac semimetals enables the study of the properties of chiral quasi-particles in three spatial dimensions. As demonstrated by photoemission, Dirac semimetals are characterized by a linear dispersion relation for fermion quasi-particles, and thus represent three dimensional analogs of graphene. While the distinctive behavior of chiral fermions (e.g. Klein tunneling) is already evident in two dimensional graphene, the physics of chirality in three dimensions opens a number of new possibilities. In this paper we investigate the properties of the collective plasmon excitations in Dirac semimetals by using the methods of relativistic field theory. We find a strong and narrow plasmon excitation whose frequency is in the terahertz (THz) range which may be important for practical applications. The properties of the plasmon appear universal for all Dirac semimetals, due to the large degeneracy of the quasi-particles and the small Fermi velocity, $v_F \ll c$. This universality is closely analogous to the phenomenon of "dimensional transmutation", that is responsible for the emergence of dimensionful scales in relativistic field theories such as Quantum Chromodynamics, the modern theory of nuclear physics.