Robust marginal Fermi liquid in birefringent semimetals

Highlights: • We investigate the interplay of Coulomb interactions and correlated disorder in pseudospin-3/2 semimetals. • Both for the 2d and 3d cases, Coulomb interactions drive the system to a marginal Fermi liquid. • We analyze if this non-Gaussian fixed point survives after the addition of disorder. • We treat disorder on an equal footing with the Coulomb terms, and re-derive the RG equations in the presence of disorder vertices. • The stable fixed points of the RG equations show that the marginal Fermi liquid is robust against disorder. We investigate the interplay of Coulomb interactions and correlated disorder in pseudospin-3/2 semimetals, which exhibit birefringent spectra in the absence of interactions. Coulomb interactions drive the system to a marginal Fermi liquid, both for the two-dimensional (2d) and three-dimensional (3d) cases. Short-ranged correlated disorder in 2d, or a power-law correlated disorder 3d, has the same engineering dimension as the Coulomb term, in a renormalization group (RG) sense. In order to analyze the combined effects of these two kinds of interactions, we apply a dimensional regularization scheme and derive the RG flow equations. The results show that the marginal Fermi liquid phase is robust against disorder.