Abstract

Owing to a power-law anisotropy in the quasiparticle dispersion, yielding an enhanced density of states, the effects of long-range Coulomb interaction get amplified in three-dimensional generalized Weyl semimetals, characterized by integer monopole charge n> 1 of the underlying Weyl nodes. Using a Wilsonian renormalization group approach controlled by a large-N expansion with N as the number of Weyl fermion flavors and a gauge-consistent regularization fixed by the Ward-Takahashi identity, we uncover for n >= 2 an extended interaction-dominated scaling regime with intrinsically anisotropic dynamic Coulomb screening, a finite fermionic anomalous dimension, and a power-law suppression of the quasiparticle residue, yielding an anisotropic marginal non-Fermi liquid at intermediate energies. Ultimately, the effective fine structure constant flows to zero, albeit only logarithmically slowly, so the marginal Fermi liquid phenomenology emerges as a broad crossover, controlled by a slowly running coupling. By contrast, for n = 1 the system retains an isotropic marginal Weyl-liquid character. These predictions can be tested via scaling in thermodynamics (specific heat and compressibility), direction-dependent optical conductivity, and by anisotropic broadening of the single-particle spectral function in angle-resolved photoemission spectroscopy.