Competition between disorder and interaction effects in three-dimensional Weyl semimetals

We investigate the low-energy scaling behavior of an interacting three-dimensional (3D) Weyl semimetal in the presence of disorder. In order to achieve a renormalization group analysis of the theory, we first focus on the effects of a short-ranged-correlated disorder potential, checking nevertheless that this choice is not essential to locate the different phases of the Weyl semimetal. We show that there is a line of fixed points in the renormalization group flow of the interacting theory, corresponding to the disorder-driven transition to a diffusive metal phase. Along that boundary, the critical disorder strength undergoes a strong increase with respect to the noninteracting theory, as a consequence of the unconventional screening of the Coulomb and disorder-induced interactions. The complementary resolution of the Schwinger-Dyson equations allows us to determine the full phase diagram of the system, showing the prevalence of a renormalized semimetallic phase in the regime of intermediate interaction strength, and adjacent to the non-Fermi liquid instability of 3D Weyl semimetals in the strong interaction regime.