Breakdown of Fermi liquid theory in topological multi-Weyl semimetals

Fermi liquid theory works very well in most normal metals, but is found violated in many strongly correlated electron systems, such as cuprate and heavy-fermion superconductors. A widely accepted criterion is that, the Fermi liquid theory is valid when the interaction-induced fermion damping rate approaches zero more rapidly than the energy. Otherwise, it is invalid. Here, we demonstrate that this criterion breaks down in topological double-and triple-Weyl semimetals. Renormalization group analysis reveals that, although the damping rate of double- and triple-Weyl fermions induced by the Coulomb interaction approaches zero more rapidly than the energy, the quasiparticle residue vanishes and the Fermi liquid theory is invalid. This behavior indicates a weaker-than-marginal violation of the Fermi liquid theory. Such an unconventional non-Fermi liquid state originates from the special dispersion of double- and triple-Weyl fermions, and is qualitatively different from all the other Fermi-liquid and non-Fermi-liquid states. The predicted properties of the fermion damping rate and the spectral function can be probed by the angle-resolved photoemission spectroscopy. The density of states, specific heat, and conductivities are also calculated and analyzed after incorporating the corrections induced by the Coulomb interaction.