The Single-Mode Approximation for Chern Bands*

The single-mode approximation (SMA) provides a tool for studying the collective excitations and the stability of the many-body gap in fractional quantum Hall (FQH) systems. In the SMA, one considers trial excitations in the form of density operators projected to the relevant single-particle bands, which for FQH systems are Landau levels. We extend this analysis by considering projection to more general Chern bands. We find that the structure factor of a Chern band factors into universal/Landau level and non-universal/lattice pieces. This allows analytical study of collective excitation gap in fractional Chern insulator (FCI) states when perturbative expansion of the Chern bands is possible. We discuss connections between the SMA and quantum geometry of single-particle bands.