TY - JOUR

T1 - Magnetic Bloch theorem and reentrant flat bands in twisted bilayer graphene at 2π flux

AU - Herzog-Arbeitman, Jonah

AU - Chew, Aaron

AU - Bernevig, B. Andrei

N1 - Publisher Copyright:
© 2022 US. Published by the American Physical Society.

PY - 2022/8/15

Y1 - 2022/8/15

N2 - 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 paper. We construct gauge-invariant irreps of the magnetic translation group at 2π 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 2π flux under the Coulomb interaction.

AB - 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 paper. We construct gauge-invariant irreps of the magnetic translation group at 2π 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 2π flux under the Coulomb interaction.

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U2 - 10.1103/PhysRevB.106.085140

DO - 10.1103/PhysRevB.106.085140

M3 - Article

AN - SCOPUS:85137685296

SN - 2469-9950

VL - 106

JO - Physical Review B

JF - Physical Review B

IS - 8

M1 - 085140

ER -