Dispersive Band Structures of Composite Fermions

Composite fermions (CFs) provide a powerful framework for understanding the fractional quantum Hall effect (FQHE), where quasiparticles form flat effective Landau levels and exhibit anyonic braiding. Recent discoveries of the fractional quantum anomalous Hall effect (FQAHE)—its zero-field analogue—raise the question of whether similar CF quasiparticles underlie these states. Interestingly, recent numerical studies indicate that anyon excitations in the FQAHE can be dispersive even when the electron band is flat, challenging the conventional CF picture. In this work, we demonstrate that CF theory can indeed accurately capture dispersions in anyon excitations that originate from electronic interactions in toy models with nonuniform magnetic fields and extend the analysis to ideal Chern bands relevant to FQAHE systems. Our results shed insights on the validity of CF theory beyond the Landau-level limit and reveal that dispersive CF bands naturally define a quantum geometry for quasiparticle states, opening new pathways toward interaction-driven non-Abelian phases through engineering the Fermi surfaces of the CF liquid.