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 - Funding Information:
We thank Zhi-Da Song and Dmitri Efetov for their insight. B.A.B. and A.C. were supported by the ONR Grant No. N00014-20-1-2303, DOE Grant No. DESC0016239, the Schmidt Fund for Innovative Research, Simons Investigator Grant No. 404513, the Packard Foundation, the Gordon and Betty Moore Foundation through Grant No. GBMF8685 towards the Princeton theory program, and a Guggenheim Fellowship from the John Simon Guggenheim Memorial Foundation. Further support was provided by the NSF-MRSEC Grant No. DMR-1420541 and DMR-2011750, BSF Israel US Foundation Grant No. 2018226, and the Princeton Global Network Funds. J.H.-A. is supported by a Marshall Scholarship funded by the Marshall Aid Commemoration Commission.
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.

UR - http://www.scopus.com/inward/record.url?scp=85137685296&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85137685296&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.106.085140

DO - 10.1103/PhysRevB.106.085140

M3 - Article

AN - SCOPUS:85137685296

VL - 106

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 8

M1 - 085140

ER -