Anisotropic marginal Fermi liquid for Coulomb interacting generalized Weyl fermions

TL;DR

This paper investigates how long-range Coulomb interactions affect three-dimensional generalized Weyl semimetals with anisotropic dispersion, revealing an anisotropic marginal Fermi liquid behavior for monopole charge n>1 through a controlled renormalization group analysis.

Contribution

It introduces a Wilsonian renormalization group framework to analyze Coulomb interactions in anisotropic Weyl semimetals, uncovering a novel anisotropic non-Fermi liquid regime for n≥2.

Findings

Anisotropic marginal non-Fermi liquid behavior for n≥2

Flow of the effective fine structure constant to zero logarithmically

Distinct isotropic behavior for n=1

Abstract

Owing to the 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 $n\ge 2$ 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 \emph{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.