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arXiv · 2508.03915

Composite Fermion Theory of Fractional Chern Insulator Stability

Xiaodong Hu·Ying Ran·Di Xiao
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Abstract

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 wavefunctions 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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Xiaodong Hu, Ying Ran, Di Xiao. 2025-08-05. Composite Fermion Theory of Fractional Chern Insulator Stability. https://arxiv.org/abs/2508.03915

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