Vortexability: A unifying criterion for ideal fractional Chern insulators

Abstract

Fractional Chern insulators exhibit the fractional quantum Hall effect (FQHE) in crystalline systems, without the need for strong magnetic fields, resulting in charge fractionalization, long-range entanglement, and anyonic statistics, potentially at elevated energy scales. The lowest Landau level (LLL) hosts the FQHE, but high Landau levels and many Chern bands do not. Vortexable bands capture the essential physics of the LLL that leads to the FQHE without requiring its more fine-tuned properties, such as uniformity of Berry curvature and of charge density.