Stability of composite fermion states in Chern insulators

We analyze an existence of composite fermion (CF) states in fractional Chern insulators (FCI) using exact diagonalization. The consider Chern insulator models for spinless fermions exhibit a signature of CF states at 2/5 and 3/7 filling factors. Evidences of fractional quantum Hall type phases for a region in a parameter space with larger energy gap are shown by looking at momenta of the n-fold degenerate ground state, spectral flow, quasihole excitation spectrum, and entanglement spectra. We analyze stability of phases as a function of model parameters showing strong correlation with flatness of Berry curvature.