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 and a power-law correlated disorder have the same engineering dimension as the Coulomb term, for the 2d and 3d systems, respectively, 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.
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