# Band structure engineering of ideal fractional Chern insulators

## TL;DR

This paper introduces an analytical method to design ideal fractional Chern insulator models with optimized band flatness, Berry curvature, and quantum geometry, facilitating robust and tunable lattice analogs of fractional quantum Hall systems.

## Contribution

We develop an analytical optimization scheme using holomorphic coordinates to generate prototypical FCI models with desirable topological and geometric properties, adaptable to various constraints.

## Key findings

- Models exhibit high tunability with few parameters
- Analytical truncation schemes enable practical implementation
- Designed models are robust under experimental constraints

## Abstract

As lattice analogs of fractional quantum Hall systems, fractional Chern insulators (FCIs) exhibit enigmatic physical properties resulting from the intricate interplay between single-body and many-body physics. In particular, the design of ideal Chern band structures as hosts for FCIs necessitates the joint consideration of energy, topology, and quantum geometry of the Chern band. We devise an analytical optimization scheme that generates prototypical FCI models satisfying the criteria of band flatness, homogeneous Berry curvature, and isotropic quantum geometry. This is accomplished by adopting a holomorphic coordinate representation of the Bloch states spanning the basis of the Chern band. The resultant FCI models not only exhibit extensive tunability despite having only few adjustable parameters, but are also amenable to analytically controlled truncation schemes to accommodate any desired constraint on the maximum hopping range or density-density interaction terms. Together, our approach provides a starting point for engineering ideal FCI models that are robust in the face of specifications imposed by analytical, numerical, or experimental implementation.