Abstract
The interplay among topology and interactions has been a promising path towards identifying novel phases of condensed matter beyond these predicted by the established classification paradigms. In the present work, we propose such a novel phase of matter by studying the fate of a three-dimensional Berry-dipole semimetal, lying at the topological quantum critical point separating a Hopf insulator from a trivial insulator, in the presence of long-range Coulomb interactions. Utilizing large-N_f analysis and an ε-expansion within the renormalization-group scheme, we predict the emergence of a spatially anisotropic non-Fermi liquid with enhanced Berry-dipole moment. The corresponding scaling relations of certain physical observables are derived as functions of the probed energy and temperature scale, and we conclude by providing an observational test for probing the enhanced topological features of the anisotropic non-Fermi liquid.