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.

7 + 3 pages, 7 figures

References in corpus (7)

• Non-Abelian Anyons and Topological Quantum Computation
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Kähler geometry and Chern insulators: Relations between topology and the quantum metric
• Elementary formula for the Hall conductivity of interacting systems

Cited by in corpus (36)

• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Family of ideal Chern flat bands with arbitrary Chern number in chiral twisted graphene multilayers
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
• 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
• Nontrivial quantum geometry of degenerate flat bands
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Unifying semiclassics and quantum perturbation theory at nonlinear order
• Recent Developments in Fractional Chern Insulators
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Fractional Chern insulators with a non-Landau level continuum limit
• Higher vortexability: zero field realization of higher Landau levels
• 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
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• Broken Symmetry in Ideal Chern Bands
• Electric field induced second-order anomalous Hall transport in unconventional Rashba systems
• Uniqueness of Landau levels and their analogs with higher Chern numbers
• Fractional Chern insulator states in an isolated flat band of zero Chern number
• Parafermions in Moiré Minibands
• Constructing vortex functions and basis states of Chern insulators: ideal condition, inequality from index theorem, and coherent-like states on von Neumann lattice
• Entropy-Enhanced Fractional Quantum Anomalous Hall Effect
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Robust translational invariance in topological bands against lattice potentials and disorders
• How quantum fluctuations freeze a classical liquid and then melt it into a topological one
• Diamagnetic Meissner response of odd-frequency superconducting pairing from quantum geometry
• Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice
• Refining Heuristic Predictors of Fractional Chern Insulators using Machine Learning