Microscopic mechanism of anyon superconductivity emerging from fractional Chern insulators

Fractional quantum Hall (FQH) states and superconductors typically require contrasting conditions, yet recent experiments have observed them in the same device. A natural explanation is that mobile anyons give rise to superconductivity. However, realizing this requires an unusual energy hierarchy that binds minimally charged anyons, a scenario that requires an additional mechanism in a repulsive system. Here, we show that such an energy hierarchy arises naturally in fractional Chern insulators (FCIs) at fillings ν = 2/(4p∓1) when they are driven toward a quantum phase transition into a “semion crystal”—a charge density wave (CDW) with semion topological order. Near the transition, Cooper-pair correlations are enhanced, so that a charge-2e superconductor appears with doping. Using tensor network simulations of a repulsive Hubbard-Hofstadter model at ν = 2/3, we demonstrate a transition from an FCI to a robust semion crystal, identifying the semion crystal as a viable competing phase together with conventional CDW and FQH states. Our framework unifies recent approaches to anyon superconductivity, reconciles it with strong repulsion, and provides guidance for flat-band moiré materials such as twisted MoTe₂.