Twisted Bilayer Graphene at 2π Flux: Magnetic Bloch Theorem and Reentrant Correlated Insulators

In 1964, Zak's discovery of the magnetic translation group demonstrated the possibility of reentrant electronic phases when the flux through a single unit cell is 2π. For the first time, the large unit cell of twisted bilayer graphene (TBG) has made it possible to test Zak's prediction in a real material. We use a newly developed gauge-invariant formalism to determine the exact single-particle band structure, topology, and correlated insulator states of magic angle TBG at 25T. We find that the characteristic flat bands reemerge at 2π flux, but, due to the magnetic field breaking C₂T, they split and acquire nonzero Chern number. We then show that reentrant correlated insulators reappear at 2π flux driven by the Coulomb interaction, and we predict the characteristic Landau fans from their excitation spectrum. Initial experiments are consistent with these predictions. Finally, we conjecture that superconductivity can also be re-entrant at 2π flux due to an emergent Hofstadter symmetry.