Electronic properties of the Dirac and Weyl systems with first- and higher-order dispersion in non-Fermi-liquid picture

We investigate the non-Fermi-liquid behaviors of the 2D and 3D Dirac/Weyl systems with low-order and higher order dispersion. The self-energy correction, symmetry, free energy, optical conductivity, density of states, and spectral function are studied. We found that, for Dirac/Weyl systems with higher order dispersion, the non-Fermi-liquid features remain even at finite chemical potential, and they are distinct from the ones in Fermi-liquid picture and the conventional non-Fermi-liquid picture. The power law dependence of the physical observables on the energy as well as the logarithmic renormalizations due to the long-range Coulomb interaction are showed. The Landau damping of the longitudinal excitations within random-phase-approximation (RPA) for the non-Fermi-liquid case are also discussed.