Non-Fermi liquid and Weyl superconductivity from the weakly interacting 3D electron gas at high magnetic fields

TL;DR

This paper explores the complex phases of 3D electron gases in high magnetic fields, revealing stable non-Fermi liquids, nematic charge density waves, and a novel layered Weyl superconductor, broadening understanding of high-field electron behavior.

Contribution

It introduces new stable phases including nematic CDWs and a layered Weyl superconductor, considering realistic interactions and symmetry breakings in high magnetic fields.

Findings

Stable nematic charge density wave with tilted quantum Hall layers.

Non-Fermi liquid phase remains stable under certain perturbations.

Discovery of a layered Weyl superconductor with unique topological properties.

Abstract

Three-dimensional electron gases in strong magnetic fields host partially flat bands that disperse along the field direction yet exhibit Landau-level quantization in the transverse dimensions. Early work established that for spin-polarized electrons confined to the lowest Landau level band, repulsion triggers a charge density wave (CDW) in which electrons 'self-layer' into integer quantum Hall states, while attraction generates a non-Fermi liquid (rather than a superconductor). We revisit this problem with physically motivated deformations -- including generalized local interactions, higher Landau level bands, restoration of spin, and explicit breaking of spatial symmetries -- paying particular attention to the competition between CDWs and superconductivity. Our main findings are: (1) Generic local interactions can stabilize a nematic CDW in which integer quantum Hall layers spontaneously 'tilt', yielding unconventional Hall response. (2) We numerically establish that the non-Fermi liquid appears stable to perturbations that preserve effective dipole conservation symmetries that emerge within a Landau level band. (3) Upon explicitly breaking translation symmetry, attraction catalyzes a novel layered superconductor that hosts Weyl nodes, superconducts within each layer, and insulates transverse to the layers. These results expand the rich phenomenology of interacting bulk electrons in the high-field regime and potentially inform the design of field-resistant superconductivity in low-carrier-density materials.