Topological Lattice Models with Constant Berry Curvature

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, equivalently, we show that the density algebra of Landau levels cannot be realised in any tight-binding lattice system.

arXiv comment7 + 3 pages, 7 figures

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• Fluctuations, uncertainty relations, and the geometry of quantum state manifolds
• Quantum Metric Induced Phases in Moiré Materials
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
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• Quantum Geometric Kohn-Luttinger Superconductivity
• Quantum Geometry and Stabilization of Fractional Chern Insulators Far from the Ideal Limit
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• Isolated flat bands in 2D lattices based on a novel path-exchange symmetry
• Enhanced quantum metric due to vacancies in graphene
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• Uniqueness of Landau levels and their analogs with higher Chern numbers
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• Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning