Anyons are fractionalized quasiparticles arising from topologically ordered systems. When an Avogadro’s number of anyons are induced, they can give rise to superfluidity by unbinding the statistical flux from the composite fermions and then putting the fermions into gapped quantum Hall states according to the filling fraction. Despite its conceptual simplicity, several key questions remain: under what conditions is this state energetically favored over other daughter phases of anyons, especially in the presence of disorder and thermal noise? Which systems are suitable for realizing such states?

In [1], we address these questions: Near topological critical points associated with band-closing transitions of the fermions describing anyon–flux composites, anyon superfluidity is highly likely upon doping. Specifically, we show that the anyon superfluid exhibits anomalously soft energy and large stiffness. Moreover, in the presence of disorder, the critical doping concentration vanishes as the critical point is approached. These exotic features, inferred from asymptotically exact field-theoretical analysis, are fundamentally determined by the conformal invariance of the QED3–Chern–Simons theory describing the critical point. We propose bilayer quantum Hall systems as ideal platforms to study this physics. We identify the direct transition between the Halperin (330) and (112)$ states at balanced filling $1/3+1/3$, observed in recent experiments and numerics, as such a critical point. Doping the layer pseudospin can lead to an anyon superfluid of excitons with the predicted characteristics. 

In [2], we analyzed transport data from a recent experiment reporting superconductivity adjacent to the anomalous fractional quantum Hall state in twisted MoTe2, finding that all observations align with the expectations of anyon superconductivity—providing promising evidence for this mechanism in real materials.