Re-entrant magic-angle phenomena in twisted bilayer graphene in integer magnetic fluxes

Abstract: In this work we address the re-entrance of magic-angle phenomena (band flatness and quantum-geometric transport) in twisted bilayer graphene (TBG) subjected to strong magnetic fluxes $\pm \Phi_0$, $\pm 2 \Phi_0$, $\pm 3 \Phi_0$... ($\Phi_0 = h/e$ is the flux quantum per moir\'e cell). The moir\'e translation invariance is restored at the integer fluxes, for which we calculate the TBG band structure using accurate atomistic models with lattice relaxations. Similarly to the zero-flux physics outside the magic angle condition, the reported effect breaks down rapidly with the twist. We conclude that the magic-angle physics re-emerges in high magnetic fields, witnessed by the appearance of flat electronic bands distinct from Landau levels, and manifesting non-trivial quantum geometry. We further discuss the possible flat-band quantum geometric contribution to the superfluid weight in strong magnetic fields (28 T at 1.08$^\circ$ twist), according to Peotta-T\"{o}rm\"{a} mechanism.