Magnetic Bloch Theorem and Reentrant Flat Bands in Twisted Bilayer Graphene at $2\pi$ Flux

Abstract

Bloch's theorem is the centerpiece of topological band theory, which itself has defined an era of quantum materials research. However, Bloch's theorem is broken by a perpendicular magnetic field, making it difficult to study topological systems in strong flux. For the first time, moiré materials have made this problem experimentally relevant, and its solution is the focus of this work. We construct gauge-invariant irreps of the magnetic translation group at $2\pi$ flux on infinite boundary conditions, allowing us to give analytical expressions in terms of the Siegel theta function for the magnetic Bloch Hamiltonian, non-Abelian Wilson loop, and many-body form factors. We illustrate our formalism using a simple square lattice model and the Bistritzer-MacDonald Hamiltonian of twisted bilayer graphene, obtaining reentrant ground states at $2\pi$ flux under the Coulomb interaction.

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• Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides
• Topological heavy fermions in magnetic field
• Double and Quadruple Flat Bands tuned by Alternative magnetic Fluxes in Twisted Bilayer Graphene
• Revisiting Bloch electrons in magnetic field: Hofstadter physics via hybrid Wannier states
• Helical trilayer graphene in magnetic field: Chern mosaic and higher Chern number ideal flat bands
• Uniqueness of Landau levels and their analogs with higher Chern numbers
• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Correlated phases and topological phase transition in twisted bilayer graphene at one quantum of magnetic flux
• Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice
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• Floquet Hofstadter butterfly in trilayer graphene with a twisted top layer
• Gap labeling theorem for multilayer thin film heterostructures
• The tuning of para- and diamagnetic cavity photon excitations in a square array of quantum dots in a magnetic field
• Orbital magnetization reveals multiband topology
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