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

Abstract: 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 moir\'e 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. Using the Landau level framework, we identify the amplification of pseudopotentials as the microscopic origin of the observed enhancement. This finding demonstrates that pseudopotential engineering can substantially strengthen fractional topological phases. We further examined non-Abelian states and found that, within finite-size resolution, this wavefunction construction method can also be used to manipulate and enhance the gap for certain interaction parameters.