Fractionalization and Superconductivity in flat Chern bands

Superconductivity and the fractional quantum Hall effect have long been considered incompatible, as the strong magnetic fields required for fractionalization typically destroy superconductivity. Yet recent experiments, for example in rhombohedral graphene and twisted MoTe₂, reveal superconductivity that breaks time-reversal symmetry and coexists with the fractional quantum anomalous Hall effect, overturning this conventional wisdom.

We will present recent theoretical developments [1,2] that uncover a unified framework connecting superconductivity and fractionalization, offering fresh insights into the interplay between these seemingly distinct phases. We will show how, starting from a purely non-perturbative problem, how fluctuations of the quantum geometry give rise to a Fermi surface and an emergent f-wave attraction arise, minimizing short-range repulsion while maximizing the pairing energy gain. The resulting phase is a chiral f-wave superconductor that hosts Majorana zero modes both at vortex cores and along the sample edges.

[1] D. Guerci*, A. Abouelkomsan*, L. Fu, From Fractionalization to Chiral Topological Superconductivity in Flat Chern Band, arXiv:2506.10938 (2025) (To appear in PRL as Editors Suggestion)

[2] D. Guerci*, A. Abouelkomsan*, L. Fu, Moiré Superconductivity with Spontaneous Vortex Lattice, arXiv:25XX.XXXXX

(*These authors contributed equally to this work.)