Multiple topological transitions in magic angle twisted bilayer graphene II

Recent experiments have observed strongly correlated physics in twisted bilayer graphene (TBG) at very small angles θ₀ = 1.05, along with nearly flat electron bands (FBs) at certain fillings. A good starting point to understand this is a continuum model [PNAS 108, 12233 (2011)] which successfully predicts the formation of FBs at θ₀. Following this work, we investigate the low energy FB structure in the entire moiré Brillouin zone (mBZ) as twisting angle is changed; the effect of transverse lattice distortion is also considered. We notice that the bands remain almost flat within a small range around θ₀, where multiple topological transitions occur. In addition to the previous understanding that the FBs are caused by the highly renormalized dispersion at K, we propose that there are other mBZ regions responsible for the low energy physics and the FBs. We trace the evolution of the Dirac points (DPs), which are very sensitive to the twist angle, and specify several processes of DP transfer within the mBZ. Furthermore, we study the effect of magnetic field to the system; comparison to the experimental results is given.