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

Jonah Herzog-Arbeitman, Aaron Chew, B. Andrei Bernevig

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish (US)
Article number085140
JournalPhysical Review B
Issue number8
StatePublished - Aug 15 2022

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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