Composite Fermion Theory Explains Fractional Chern Insulators with Filling Factors of 1/3 and 2/3

Fractional Chern insulators represent a fascinating state of matter where interactions between electrons give rise to emergent phenomena, and understanding their behaviour remains a significant challenge in condensed matter physics. Hao Jin and Junren Shi, both from Peking University, present a new theoretical framework that extends the established composite fermion theory to better describe these complex materials. Their work clarifies how composite fermions, which emerge from interacting electrons, experience the unique properties of fractional Chern insulators, effectively mapping the behaviour of electrons onto that of these quasiparticles. This generalized approach not only provides a more accurate description of existing materials, such as twisted bilayer MoTe, but also predicts a connection between the fractional Chern insulator state and the topological properties of the underlying composite fermion bands, offering new avenues for materials discovery and design.

Composite Fermions and Fractional Quantum Hall States

The foundation of this work lies in understanding strongly correlated electron systems and the fractional quantum Hall effect, a quantum phenomenon observed in two-dimensional materials. The central idea involves describing these systems using composite fermions, which are quasiparticles formed by combining electrons with magnetic flux quanta. This simplification allows researchers to tackle complex many-body problems, often reducing them to more manageable single-particle scenarios. Key to this understanding are concepts like the fractional quantum Hall effect, where electrons exhibit quantized conductance values that are fractions of a fundamental unit.

Composite fermions are crucial as they effectively reduce the strength of interactions between electrons, potentially leading to new phases of matter. The magnetic translation operator describes how electron wavefunctions shift in a magnetic field and is essential for constructing the composite fermion wavefunctions. The Laughlin wavefunction provides a foundational description of the ground state of the fractional quantum Hall effect, while Landau levels represent the quantized energy levels of electrons in a magnetic field. Berry curvature and the metric tensor, geometric properties of energy bands, also play a role in determining the effective magnetic field experienced by electrons. The reduced magnetic Brillouin zone simplifies calculations in a magnetic field, and the filling fraction, the ratio of electrons to magnetic flux quanta, dictates the electronic properties of the system.

Composite Fermions Explain Chern Insulator Behaviour

This research successfully applies the generalized composite fermion theory to fractional Chern insulators, accurately reproducing key features observed in numerical calculations. The results demonstrate that the composite fermion theory accurately captures trends in the system’s energy gaps and phase boundaries, with the electron-based model showing particularly strong agreement with existing data. Importantly, the analysis reveals a connection between the fractional Chern insulator phase transition and changes within the unoccupied composite fermion bands, suggesting that the topological properties of these bands may drive the transition itself. While the study successfully models several aspects of the system, the authors acknowledge a limitation in the theory’s inability to fully account for periodic potentials experienced by vortices, which may explain discrepancies between the electron and hole-based models. Future work, alongside a related study by other researchers, will likely focus on refining the model and further exploring the topological transitions of these bands to better understand and predict the stability of fractional Chern insulators. This research complements existing findings by concentrating on the construction and transitions of specific bands and their impact on FCI stability.