Revisiting the fate of interacting 3D semimetals in the ultra-quantum limit

Low-carrier-density bulk materials such as Weyl semimetals can enter the ultra-quantum limit—wherein a single Landau level band is populated—at experimentally accessible magnetic fields. In this regime, the interplay between Landau level degeneracy, residual kinetic energy along the field direction, and repulsive interactions has been shown to generate a "self-layering" charge-density wave instability realizing a three-dimensional integer quantum hall state. We revisit the fate of semimetals in the ultra-quantum limit using functional renormalization group techniques, allowing for general symmetry-allowed bare interactions. In addition to the familiar charge density waves, our treatment captures Wigner-crystal-like instabilities in which electrons organize into arrays of "tubes" oriented along the field. We also investigate the stability of the marginal Fermi liquid state previously found to emerge from attractive interactions.