Effects of Berry curvature on ideal fractional Chern insulator many-body gaps

We investigate the many-body ground states in a family of fractionally filled bands where the Berry curvature fluctuations can be tuned while maintaining ideal quantum geometry. We numerically find that the neutral gap of the fractional Chern insulator (FCI) ground state decreases as the Berry curvature becomes less homogeneous, ultimately driving an instability to a charge density wave. We further extend our analysis to bands perturbed away from the ideal limit and give examples where a less ideal band geometry results in a more stable FCI phase. To explain our findings, we apply the single-mode approximation to the ground-state wave functions of the ideal band, from which we obtain analytic expressions for the FCI many-body gap in the limit of weak Berry curvature variations. Finally, we make a connection between our results and experimentally relevant systems where FCIs have been observed.