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.
Cited by 3
Mera et al., Nontrivial quantum geometry of degenerate flat bands
Phys. Rev. B 106, 165133 (2022) [Crossref]
Northe et al., Interplay of band geometry and topology in ideal Chern insulators in the presence of external electromagnetic fields
Phys. Rev. B 105, 155410 (2022) [Crossref]
Wang et al., Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
Phys. Rev. Lett. 128, 176403 (2022) [Crossref]
Authors / Affiliation: mappings to Contributors and OrganizationsSee all Organizations.
- Knut och Alice Wallenbergs Stiftelse (Knut and Alice Wallenberg Foundation) (through Organization: Knut och Alice Wallenbergs Stiftelse / Knut and Alice Wallenberg Foundation)
- Vetenskapsrådet / Swedish Research Council