Higher vortexability: zero field realization of higher Landau levels

Abstract

The rise of moiré materials has led to experimental realizations of integer and fractional Chern insulators in small or vanishing magnetic fields. At the same time, a set of minimal conditions sufficient to guarantee a Abelian fractional state in a flat band were identified, namely "ideal" or "vortexable" quantum geometry. Such vortexable bands share essential features with the lowest Landau level, while excluding the need for more fine-tuned aspects such as flat Berry curvature. A natural and important generalization is to ask if such conditions can be extended to capture the quantum geometry of higher Landau levels, particularly the first (1LL), where non-Abelian states at $\nu =1/2,2/5$ are known to be competitive. The possibility of realizing these states at zero magnetic field , and perhaps even more exotic ones, could become a reality if we could identify the essential structure of the 1LL in Chern bands. In this work, we introduce a precise definition of 1LL quantum geometry, along with a figure of merit that measures how closely a given band approaches the 1LL. We apply the definition to identify two models with 1LL structure -- a toy model of double bilayer twisted graphene and a more realistic model of strained Bernal graphene.

12 pages, 5 figures

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• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene
• Intraband collective excitations in fractional Chern insulators are dark
• Quantum geometric bounds for observables: Linear responses, Drude weight, and orbital magnetization
• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Symmetry-based classification of exact flat bands in single and bilayer moiré systems
• Coexisting Kagome and Heavy Fermion Flat Bands in YbCr${}_6$Ge${}_6$
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions
• Quantum geometric tensors from sub-bundle geometry
• Quantum phase diagram and non-abelian Moore-Read state in double twisted bilayer graphene
• Electronic bounds in magnetic crystals
• Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory
• Relaxation toward an Ideal Chern Band through Coupling to a Markovian Bath
• Buckling and flat bands in twisted bilayer graphene
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• Robustness of real-space topology in moiré systems
• Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice
• Orbital Description of Landau Levels