Abstract

Unconventional superconductivity beyond phonon-mediated pairing has long been a central theme in condensed matter physics, and in the late 1980s Laughlin proposed the striking idea of "anyon superconductivity," which stalled because anyons were never identified in cuprates. In this talk I describe how moiré materials revive this mechanism: their fractional Chern insulator (FCI) states host anyonic excitations, and superconductivity is repeatedly observed in close proximity. Using large-scale numerics in the lowest Landau level with a periodic potential, we show that purely repulsive interactions can produce a spinless chiral f-wave superconductor and reveal a continuous transition from an FCI to a superconductor, strongly pointing to an anyon-driven route rather than conventional pairing. We then formulate modern critical field theories (QED3–Chern–Simons and QCD3–Chern–Simons) that place Laughlin's proposal in contemporary language and provide a controlled framework for a strongly correlated pathway to superconductivity.