Nematicity and superconductivity in rhombohedral graphene

Motivated by reports of superconductivity concurrent with anisotropic transport and CDW order in rhombohedral multilayer graphene [1], we analyze pairing instabilities of the quarter‑metal state in rhombohedral hexalayer graphene using a continuum model. Building on self‑consistent mean‑field solutions that yield a single anisotropic Fermi surface with strongly asymmetric Berry curvature, we formulate the linearized gap equation accounting for Bloch‑spinor form factors. We show that rapid spinor variation (large local Berry curvature) makes small‑momentum components of the Coulomb interaction less repulsive, providing a natural route to Kohn–Luttinger–type instabilities without phonons. We map the angular‑momentum content and momentum structure of the leading eigenmodes and identify how displacement field, carrier density, and nematicity bias the competition between zero‑q and finite‑q channels. We outline experimental consequences for anisotropic critical fields, nonreciprocal transport, and phase‑sensitive probes. Our results clarify how band geometry and flavor polarization steer unconventional pairing in non‑moiré rhombohedral multilayer graphene. 

[1] Nguyen, R. Q., H.-T. Wu, E. Morissette, N. J. Zhang, P. Qin, K. Watanabe, T. Taniguchi, A. W. Hui, D. E. Feldman, and J. I. A. Li, “A hierarchy of topological and superconducting states in rhombohedral hexalayer graphene,” arXiv:2507.22026 (2025).