Recent experiments reported evidence of superconductivity and reentrant integer quantum anomalous Hall (RIQAH) insulator upon doping the ${\nu }_e=2/3$ fractional quantum anomalous Hall states (FQAHs) in twisted ${\mathrm{MoTe}}_2$, separated by narrow resistive regions. Anyons of an FQAH generally have a finite effective mass and, when described by anyon-flux composite fermions (CFs), experience statistical magnetic fields with a commensurate filling. Here, we show that most of the experimental observations can be explained by invoking the effects of disorder on the Landau-Hofstadter bands of CFs. In particular, by making minimal assumptions about the anyon energetics and dispersion, we show that doping anyons drives plateau transitions of CFs into integer quantum Hall states, which physically corresponds to either a superconductor or to an RIQAH phase. We develop a dictionary that allows us to infer the response in these phases and the critical regions from the knowledge of the response functions of the plateau transitions. In particular, this allows us to relate the superfluid stiffness of the superconductor to the polarizability of CFs. As a first step toward a quantitative understanding, we borrow results from the celebrated integer quantum Hall plateau transitions to make quantitative predictions for the critical behavior of the superfluid stiffness, longitudinal and Hall conductivity, and response to out-of-plane magnetic field, all of which agree reasonably well with the experimental observations. Our results provide strong support for anyon superconductivity being the mechanism for the observed superconductor in the vicinity of the ${\nu }_e=2/3$ FQAH insulator.

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• Anyons
• Composite fermions
• Fractional quantum Hall effect
• Superconductivity
• Superconductor-insulator transition
• Chern insulators
• Chern-Simons gauge theory
• Effective field theory