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 ${\mathrm{MoTe}}_2$ 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.

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• Composite fermions
• Fractional quantum Hall effect
• Quantum anomalous Hall effect
• Topological order
• Twisted heterostructures
• Projective symmetries
• Trial wave functions