Single-component twisted $\mathbb{Z}_3$ orthogonal metal in an $e/3$-anyon fluid

We propose an unconventional metallic phase emerging on doping the $1/3$ Fractional Chern insulator, which can serve as a parent state to anyon superconductivity with arbitrary chiral central charge. It is a twisted $\mathbb{Z}_3$ orthogonal metal: a state with vanishing electron quasiparticle weight but a single well-defined Fermi surface of emergent charge-$e/3$ fermions coupled to a Dijkgraaf-Witten twisted $\mathbb{Z}_3$ gauge field. It is manifestly valley-symmetric and valley-gapped. Pairing this fractionalized Fermi surface then removes the topological order and produces a family of superconductors whose chiral central charge is directly set by the BdG band topology of the paired $e/3$ fermions, while the angular momentum of the physical order parameter is constrained to be a multiple of three. This scenario provides a route to superconducting states beyond anyon-superconductivity constructions based on $2e/3$ anyons. The metallic phase itself carries distinctive ``fractional Fermiology'' signatures: $e/3$ shot noise, anomalous quantum oscillations, and a $6\pi$ ac Josephson effect when it mediates the Josephson coupling between superconductors. We construct explicit wavefunction ansatz realizing the phase, and argue that inter-valley repulsion between anyons stabilizes this phase compared to competing states. We show that the construction extends to higher Laughlin states but not to Jain states.