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Fermi liquid theory works very well in most normal metals, but is foundviolated in many strongly correlated electron systems, such as cuprate andheavy-fermion superconductors. A widely accepted criterion is that, the Fermiliquid theory is valid when the interaction-induced fermion damping rateapproaches zero more rapidly than the energy. Otherwise, it is invalid. Here,we demonstrate that this criterion breaks down in topological double-andtriple-Weyl semimetals. Renormalization group analysis reveals that, althoughthe damping rate of double- and triple-Weyl fermions induced by the Coulombinteraction approaches zero more rapidly than the energy, the quasiparticleresidue vanishes and the Fermi liquid theory is invalid. This behaviorindicates a weaker-than-marginal violation of the Fermi liquid theory. Such anunconventional non-Fermi liquid state originates from the special dispersion ofdouble- and triple-Weyl fermions, and is qualitatively different from all theother Fermi-liquid and non-Fermi-liquid states. The predicted properties of thefermion damping rate and the spectral function can be probed by theangle-resolved photoemission spectroscopy. The density of states, specificheat, and conductivities are also calculated and analyzed after incorporatingthe corrections induced by the Coulomb interaction.

Breakdown of Fermi liquid theory in topological multi-Weyl semimetals