Multiple topological transitions in magic angle twisted bilayer graphene I

The physics of twisted bilayer graphene (TBG) structures has attracted a lot of interest experimentally and theoretically. Attention was drawn to these systems largely by recent experimental works, which showed strong correlation effects in bilayer graphene systems with a twist angle of roughly 1°, the so-called magic angle. A continuum model for describing such systems is used in our study, and instead of observing flat bands only at the magic angle, we notice that the bands remain almost flat within a small range around the magic angle, where multiple topological transitions occur. The topological transitions are caused by creation and annihilation of Dirac points, which are transported within the moire Brillouin zone as the angle is varied around the magic angle. Furthermore, we propose an effective low energy six-band model near the Γ point, which we argue is the minimal model to explain the motion of the Dirac points around Γ as the angle is varied. These observations can also be exploited for explaining the experimental results regarding the response of the magic angle TBG systems to external magnetic field.