We propose a generalized composite fermion (CF) theory for fractional Chern insulators (FCIs) by adapting the quantum mechanics approach of CFs. The theoretical framework naturally produces an effective CF Hamiltonian and a wave-function ansatz, and the Bloch band characteristics of FCIs determine effective scalar and vector potentials experienced by CFs. Our analysis clarifies the construction of CF wave functions and state counting in CF phase space, which is subject to a density-of-states correction. We apply the theory to study the $\nu =-2/3$ FCI state of the twisted bilayer ${\mathrm{MoTe}}_2$ system, modeling it as either a $1/3$-filled electron band or a $2/3$-filled hole band. While both CF models exhibit trends and features consistent with exact diagonalization results, the electron-based model shows better agreement. Furthermore, we find that the FCI phase transition coincides with a gap closure in unoccupied CF $\mathrm{\Lambda }$ bands. This coincidence suggests that changes in CF excitons, such as CF-roton softening, may drive the transition.

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• Composite fermions
• Fractional quantum Hall effect
• Chern insulators
• Strongly correlated systems
• Exact diagonalization
• Mean field theory