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

TL;DR

This work analyzes a weakly interacting three-dimensional electron gas in a strong magnetic field, focusing on the competition between density-wave orders and superconductivity within partially flat Landau-level bands. Using an extended functional RG framework that includes higher Landau levels, spin, and symmetry-breaking perturbations, it identifies a nematic topological CDW, a robust non-Fermi liquid, and, under explicit translation-symmetry breaking, a Weyl-layered superconductor with Weyl Bogoliubov nodes. The NFL phase remains stable when effective dipole conservation in a Landau level is preserved, while breaking translation symmetry converts the system into a layered superconductor with interlayer Josephson couplings that respect dipole constraints but permit edge transport. These results broaden the landscape of high-field bulk electron phenomena and hint at design principles for field-resistant superconductivity in low-carrier-density materials, with clear experimental signatures in Hall physics, CDW tilt, and Bogoliubov Weyl nodes.

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.

Figures (9)

• Figure 1: Flat Fermi surface of the non-interacting three-dimensional electron gas in a strong magnetic field. The blue arrows indicate BCS-type superconducting instabilities and the orange arrows indicate charge density wave instabilities.
• Figure 2: Typical renormalized coupling functions for the three phases discussed in this section, evaluated using the bare coupling (\ref{['eqn:g0g1']}) with $(g_0,g_1) = (1,0)$ for the blue curve, $(0,1)$ for the orange curve, and $(-1,0)$ for the green curve. The bottom panel is the two-dimensional Fourier transform (Hankel transform) of the top panel.
• Figure 3: Phase diagram for the weakly interacting three-dimensional electron gas in the lowest Landau level determined via numerical integration of the flow equations. The horizontal axis represents the contact density-density interaction studied previously Yakovenko1993, while the vertical axis represents a higher derivative interaction [Eq. (\ref{['eq:g1']})] that enables a nematic integer quantum Hall charge density wave phase. A qualitatively similar phase diagram emerges when projecting those interactions into the second Landau level instead of the lowest Landau level.
• Figure 4: Stability of the non-Fermi liquid phase to rotation-symmetry-breaking perturbations encoded in the bare coupling function from Eq. (\ref{['eqn:anisotropic']}) when $\lambda_1 \neq \lambda_2$. Here, the "tilted" phase is not a nematic as the rotation symmetry is explicitly broken; it only spontaneously breaks the residual $\mathbb{Z}_2$ symmetry of $\pi$ rotations.
• Figure 5: RG flow of the spinful interacting lowest Landau level. The phase boundary resembles the separatrix of the Berezinskii-Kosterlitz-Thouless flow equations (dotted line added for visualization) ending at $w_0 = 0, v_0 = u_0$ as predicted by a naive two-channel Luttinger liquid description (\ref{['eqn:Hspin']}).