Recent experiments have observed superconductivity proximate to the $\nu =-2/3$ fractional quantum anomalous Hall (FQAH) insulator in twisted ${\mathrm{MoTe}}_2$. A critical open question is whether the underlying normal state is a Fermi liquid with a large Fermi surface or a strongly correlated metal with low carrier density. In this work, we develop a theory of the phases emerging from doping the $\nu =-2/3$ fractional Chern insulator (FCI). We establish a duality between this problem and doping a gapped ${\mathrm{SU}\left(3\right)}_1$ chiral spin liquid (CSL). In both scenarios, one possible metallic state upon doping is a holon metal featuring three small Fermi pockets. These pockets are formed by spinless charge $-e$ holons in the CSL case and charge $-e/3$ fractionalized holes in the FCI case. While the holon metal is susceptible to pairing instabilities driven by gauge fluctuations—leading to a charge density wave (CDW) metal—it may be stabilized by a magnetic field, where it would exhibit an anomalous quantum oscillation period. We identify two distinct chiral superconducting phases that can emerge either from the CDW metal or directly from the holon metal. Finally, we argue that superconductivity arising directly from an anyon gas is not likely if the lowest-energy anyon carries the elementary charge $e/3$.

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• Effective field theory
• Fractionalization
• Topological phases of matter
• Topological superconductors
• Chern-Simons gauge theory