Anyon delocalization transitions out of a disordered fractional quantum anomalous Hall insulator

Motivated by the experimental discovery of the fractional quantum anomalous Hall effect, we develop a theory of doping-induced transitions out of the [Formula: see text] lattice Jain state in the presence of quenched disorder. We show that disorder strongly affects the evolution into the conducting phases described in our previous work. The delocalization of charge [Formula: see text] anyons leads to a chiral superconductor through a direct second-order transition for a smooth random potential with long-wavelength modulations. The longitudinal resistance has a universal peak at the associated quantum critical point. Close to the transition, we show that the superconducting ground state is an "Anomalous Vortex Glass" stabilized in the absence of an external magnetic field. For short-wavelength disorder, this transition generically splits into three distinct ones with intermediate insulating topological phases. If instead, the charge [Formula: see text] anyon delocalizes, then at low doping the resulting phase is a Reentrant Integer Quantum Hall state with [Formula: see text]. At higher doping this undergoes a second transition to a Fermi liquid metal. We show that this framework provides a plausible explanation for the complex phase diagram recently observed in twisted MoTe₂ near [Formula: see text] and discuss future experiments that can test our theory in more detail.