# Topological Lattice Models with Constant Berry Curvature

### Submission summary

 As Contributors: Emil Bergholtz · Daniel Varjas Preprint link: scipost_202107_00047v1 Code repository: https://zenodo.org/record/5102818#.YPk3hRMza3I Date submitted: 2021-07-22 14:31 Submitted by: Varjas, Daniel Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Approaches: Theoretical, Computational

### Abstract

Band geometry plays a substantial role in topological lattice models. The Berry curvature, which resembles the effect of magnetic field in reciprocal space, usually fluctuates throughout the Brillouin zone. Motivated by the analogy with Landau levels, constant Berry curvature has been suggested as an ideal condition for realizing fractional Chern insulators. Here we show that while the Berry curvature cannot be made constant in a topological two-band model, lattice models with three or more degrees of freedom per unit cell can support exactly constant Berry curvature. However, contrary to the intuitive expectation, we find that making the Berry curvature constant does not always improve the properties of bosonic fractional Chern insulator states. In fact, we show that an "ideal flatband" cannot have constant Berry curvature.

###### Current status:
Editor-in-charge assigned