Composite Fermion Theory of Fractional Chern Insulator Stability

Area of Science:

• Condensed Matter Physics
• Quantum Materials

Background:

• Fractional Chern insulators (FCIs) are topological states of matter exhibiting exotic electronic properties.
• Understanding the stability and identification of FCIs is crucial for advancing topological quantum technologies.

Purpose of the Study:

• To develop a novel mean-field theory for predicting the stability of fractional Chern insulators.
• To provide a computationally efficient method for identifying FCIs in realistic material systems.

Main Methods:

• A mean-field theory based on the dipole picture of composite fermions (CFs) was developed.
• CFs were constructed by binding vortices to Bloch electrons, leading to a Hofstadter problem in an enlarged Hilbert space.
• The theory was applied to twisted MoTe$_{2}$ to calculate CF band structures.

Main Results:

• The derived CF Hamiltonian naturally incorporates the trace-condition term in the small-q limit.
• Calculated CF band structures for twisted MoTe$_{2}$ closely matched exact diagonalization results.
• Projected many-body wave functions showed exceptionally high overlaps with exact diagonalization results.

Conclusions:

• The developed mean-field theory offers a microscopic understanding of FCI stability.
• This theory serves as a computationally efficient tool for identifying fractional Chern insulators.