Vortexability: A unifying criterion for ideal fractional Chern insulators

Fractional Chern insulators realize the remarkable physics of the fractional quantum Hall effect (FQHE) in crystalline systems with Chern bands. The lowest Landau level (LLL) is known to host the FQHE, but not all Chern bands are suitable for realizing fractional Chern insulators (FCI). Previous approaches to stabilizing FCIs focused on mimicking the LLL through momentum-space criteria. Here, instead, we take a real-space perspective by introducing the notion of vortexability. Vortexable Chern bands admit a fixed operator that introduces vortices into any band wavefunction while keeping the state entirely within the same band. Vortexable bands admit trial wavefunctions for FCI states, akin to Laughlin states. In the absence of dispersion and for sufficiently shortranged interactions, these FCI states are the ground state-independent of the distribution of Berry curvature. Vortexable bands are much more general than the LLL, and we showcase a recipe for constructing them. We exhibit diverse examples in graphene-based systems with or without magnetic field, and with any Chern number. A special class of vortexable bands is shown to be equivalent to the momentum-space trace condition or ideal band condition. In addition, we also identify a more general form of vortexability that goes beyond this criterion. We introduce a modified measure that quantifies deviations from general vortexability, which can be applied to generic Chern bands to identify promising FCI platforms.

Automated summary

Fractional Chern insulators, a type of crystalline system with Chern bands, exhibit the physics of fractional quantum Hall effect. This study introduces the concept of vortexability from a real-space perspective to stabilize fractional Chern insulators. Vortexable Chern bands allow the introduction of vortices into any band wavefunction while remaining within the same band, enabling the realization of FCI states. These vortexable bands are more general than the lowest Landau level (LLL), and a recipe for constructing them in graphene-based systems is provided. Various examples are presented to demonstrate the effectiveness of this approach.