Spectral function of the three-dimensional system of massless Dirac electrons

We determine the one-particle spectral function for the three-dimensional system of massless Dirac electrons with the long-range Coulomb interaction. The electron self-energy is calculated within the G0W0 approximation. We find that the spectral function has a low-energy quasi-particle and a characteristic structure due to the optic plasmon mode. The present approach is appropriate for the wide range of energy scales given by Fermi energy and plasmon energy. The obtained spectral properties are brought into correspondence with the spectra of the three-dimensional topological Dirac semimetals obtained from recent angle-resolved photoemission spectroscopy (ARPES) measurements.