Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators

Abstract

Fractional Chern insulators realize the remarkable physics of the fractional quantum Hall effect (FQHE) in crystalline systems with Chern bands. The lowest Landau level (LLL) is known to host the FQHE, but not all Chern bands are suitable for realizing fractional Chern insulators (FCI). Previous approaches to stabilizing FCIs focused on mimicking the LLL through momentum space criteria. Here instead we take a real-space perspective by introducing the notion of vortexability. Vortexable Chern bands admit a fixed operator that introduces vortices into any band wavefunction while keeping the state entirely within the same band. Vortexable bands admit trial wavefunctions for FCI states, akin to Laughlin states. In the absence of dispersion and for sufficiently short ranged interactions, these FCI states are the ground state -- independent of the distribution of Berry curvature. Vortexable bands are much more general than the LLL, and we showcase a recipe for constructing them. We exhibit diverse examples in graphene-based systems with or without magnetic field, and with any Chern number. A special class of vortexable bands is shown to be equivalent to the momentum space "trace condition" or "ideal band condition". In addition, we also identify a more general form of vortexability that goes beyond this criterion. We introduce a modified measure that quantifies deviations from general vortexability which can be applied to generic Chern bands to identify promising FCI platforms.

9 pages, 3 figures main text. 26 pages, 4 figures including supplement. Corrections to example E2 of V1

References in corpus (26)

• The electronic properties of graphene
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• The electronic properties of bilayer graphene
• Fractional quantum Hall states at zero magnetic field
• All-graphene integrated circuits via strain engineering
• Fractional quantum Hall effect in the absence of Landau levels
• Lattice relaxation and energy band modulation in twisted bilayer graphenes
• Graphene as an electronic membrane
• Symmetry-based approach to electron-phonon interactions in graphene
• Chiral Decomposition in the Electronic Structure of Graphene Multilayers
• Gauge field induced by ripples in graphene
• The crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the "magic angle" $\theta \sim 1.08^{\circ }$
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Density-curvature response and gravitational anomaly
• Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
• Tunable quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene
• Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Enhancing the stability of a fractional Chern insulator against competing phases
• Theory of Nematic Fractional Quantum Hall State
• Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
• Chiral Magic-Angle Twisted Bilayer Graphene in a Magnetic Field: Landau Level Correspondence, Exact Wavefunctions and Fractional Chern Insulators
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size

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• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Instantaneous response and quantum geometry of insulators
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• Quantum Geometry and Stabilization of Fractional Chern Insulators Far from the Ideal Limit
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• Superconductivity in a Topological Lattice Model with Strong Repulsion
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• Isolated nearly flat higher Chern band in monolayer transition metal trihalides
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• Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Coexisting Kagome and Heavy Fermion Flat Bands in YbCr${}_6$Ge${}_6$
• Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The ${\lambda }_N$-Jellium model
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• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective
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