# Topological Lattice Models with Constant Berry Curvature

### Submission summary

 Authors (as Contributors): Ahmed Abouelkomsan · Emil Bergholtz · Daniel Varjas
Submission information
Code repository: https://zenodo.org/record/5102818#.YPk3hRMza3I
Date accepted: 2022-03-22
Date submitted: 2022-02-25 14:11
Submitted by: Varjas, Daniel
Submitted to: SciPost Physics
Ontological classification
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 fractional Chern insulator states. In fact, we show that an "ideal flatband" cannot have constant Berry curvature, equivalently, we show that the density algebra of Landau levels cannot be realised in any tight-binding lattice system.

Published as SciPost Phys. 12, 118 (2022)

We thank the Referees for reviewing our manuscript, and the generally positive reactions. Both referees requested clarifications of the presentation of the manuscript, so we rephrased the introduction and changed the order of sections, see the detailed list of changes below. The referees also asked to clarify our interpretation of the numerical data, as a response we added further analysis to sec VI and Fig 6. We are confident that with these changes our manuscript is sufficiently clear and meets the standards of SciPost Physics.

### List of changes

1. We rephrased the last two paragraphs of the Introduction, and added an overview of the structure of the paper, so it is easier to follow.
2. We merged sections IV and V about the constant curvature models, and moved section III with the 2-band no-go theorem after them.
3. We added further analysis of the relation of the ideal droplet condition and the FCI physics in section VI and figure 6.
4. Changes of phrasing, corrections, and clarifications throughout the manuscript.