Beyond the Lowest Landau Level: Unlocking More Robust Fractional States Using Flat Chern Bands with Higher Vortexability

Enhancing the many-body gap of a fractional state is crucial for realizing robust fractional excitations. For fractional Chern insulators, existing studies suggest that making flat Chern bands closely resemble the lowest Landau level (LLL) seems to maximize the excitation gap, providing an apparently optimal platform. In this work, we demonstrate that deforming away from the LLL limit can, in fact, produce substantially larger FQH gaps. Using moiré flat bands with strongly non-Landau-level wavefunctions, we show that the gap can exceed that of the LLL by more than two orders of magnitude for short-range interactions and by factors of two to three for long-range interactions. This enhancement is generic across Abelian FCI states and follows a universal enhancement factor within each hierarchy. By mapping the effect onto the Landau-level framework, we identify the amplification of pseudopotentials as the microscopic origin, revealing that Berry curvature and quantum geometry alone are insufficient to determine the many-body gap. Instead, pseudopotential engineering beyond the Landau paradigm can dramatically strengthen fractional topological phases.