Composite Fermion Theory of Fractional Chern Insulator Stability

We develop a mean-field theory of the stability of fractional Chern insulators based on the dipole picture of composite fermions (CFs). We construct CFs by binding vortices to Bloch electrons and derive a CF single-particle Hamiltonian that describes a Hofstadter problem in the enlarged CF Hilbert space, with the trace-condition term emerging naturally in the small-q limit as part of the CF Hamiltonian. Going beyond the small-q limit, we apply our theory to twisted MoTe_{2} and calculate its CF band structures. The resulting CF phase diagram matches closely with that from exact diagonalization, and the projected many-body wave functions achieve exceptionally high overlaps with the latter. Our theory provides both a microscopic understanding and a computationally efficient tool for identifying fractional Chern insulators.