Composite Fermion Theory of Fractional Chern Insulator Stability

TL;DR

This paper develops a mean-field composite fermion theory for fractional Chern insulators, providing a microscopic understanding and computational tool that aligns well with exact diagonalization results, especially applied to twisted MoTe2.

Contribution

It introduces a new mean-field framework based on the dipole picture of composite fermions, extending the understanding of fractional Chern insulator stability beyond small momentum limits.

Findings

CF phase diagram matches exact diagonalization results

Projected wavefunctions have high overlaps with exact solutions

Theory effectively describes CF band structures in twisted MoTe2

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.