Interplay of disorder and interactions in a system of subcritically tilted and anisotropic three-dimensional Weyl fermions

We study the effects of disorder and Coulomb interactions on the physics of three-dimensional type-I Weyl fermions with tilted and anisotropic dispersions in a renormalization-group approach. To lowest nontrivial loop order, we show that the tendency of the Coulomb interactions to restore the symmetry of the dispersion in the semimetallic region of the phase diagram dominates the stabilization of the tilt and anisotropy favored by weak disorder. We argue that the topology of the renormalization flow of the disorder and Coulomb couplings is essentially determined by gauge invariance so that these findings continue to hold qualitatively at any order in perturbation theory