Parent (half)metal and emergent superconductivity in rhombohedral trilayer graphene

Combining mean-field and renormalization group analyses, I shed light on recently observed superconductivity and their parent states in chemically doped rhombohedral trilayer graphene, subject to external electric displacement fields. I argue that close to the charge neutrality, on site Hubbard repulsion favors layer antiferromagnet, which when combined with the displacement field (inducing layer polarization), produces a spin-polarized, but valley or isospin unpolarized half-metal, conducive to the nucleation of spin-triplet  f-wave pairing. By contrast, at larger doping Kekulé valence bond order emerges as a prominent candidate for isospin coherent paramagent, boosting condensation of spin-singlet Cooper pairs in the conventional s-wave channel, manifesting a "selection rule" among competing orders. Responses of these paired states to displacement and in-plane magnetic fields show qualitative similarities with experimental observation.