Universal Aspects of the Interacting 3d Electron Gas in a Strong Magnetic Field

Strong interactions in one-dimensional systems lead to universal non-Fermi liquid behavior. A strong magnetic field in a two-dimensional electron gas, instead, alters the single-particle physics leading to Hall quantization. These seemingly distinct aspects converge in an interacting 3d electron gas in a strong magnetic field. The in-plane wavefunctions resemble those of the lowest Landau level, while the additional dimension introduces a quasi-one-dimensional dispersion along the magnetic field direction. Using Fermi surface renormalization group techniques, we revisit various instabilities of this state, focusing on the competition between charge density wave (CDW) and superconducting (BCS) instabilities. Besides finding nematic CDW states with an anomalous Hall response, we uncover a subtle relationship between magnetic translation symmetry and BCS instabilities which appears to be crucial to understanding the stability of a non-Fermi liquid state which was numerically observed in this regime. We argue that explicitly breaking translation symmetry can realize a novel layered superconducting state, whose low energy physics resembles that of a 1d dipole-conserving rotor model.