Generalizing the composite fermion theory for fractional Chern insulators

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 wavefunction ansatz, and the Bloch band characteristics of FCIs determine effective scalar and vector potentials experienced by CFs. Our analysis clarifies the construction of CF wavefunctions and state counting in CF phase space, which is subject to a density-of-states correction for filling factors $|\nu| \neq 1/2$. We apply the theory to study the $\nu=-2/3$ FCI state of the twisted bilayer 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 topological phase transition in unoccupied CF $\Lambda$-bands.