A recent milestone in condensed matter physics was the realization of the fractional quantum anomalous Hall effect (FQAHE) in moiré systems at partial fillings of the lowest topological miniband, where the lowest Landau level serves as a guiding principle. Can this principle be pushed to higher fillings, in analogy with the 1st excited Landau level? We answer this in the affirmative for a class of models, skyrmion Chern band (SCB) models, which can be realized in 2D semiconductor / chiral magnet heterostructures and also capture the essence of transition metal dichalcogenide (TMD) homobilayers. In particular, the half-filled second topological miniband of SCB models can stabilize a Moore-Read state even in the presence of strongly fluctuating Berry curvature. We discuss lessons on the desirable conditions for the non-Abelian FQAHE and implications for nonabelions in moiré systems.

On work done with Aidan P. Reddy, Ahmed Abouelkomsan, and Liang Fu (arxiv.org/abs/2403.00059)