Bistritzer–MacDonald dynamics in twisted bilayer graphene

The Bistritzer–MacDonald (BM) model, introduced by Bistritzer and MacDonald [Proc. Natl. Acad. Sci. U. S. A. 108, 12233–12237 (2011); arXiv:1009.4203], attempts to capture electronic properties of twisted bilayer graphene (TBG), even at incommensurate twist angles, by using an effective periodic model over the bilayer moiré pattern. Starting from a tight-binding model, we identify a regime where the BM model emerges as the effective dynamics for electrons modeled as wave-packets spectrally concentrated at monolayer Dirac points up to error that can be rigorously estimated. Using measured values of relevant physical constants, we argue that this regime is realized in TBG at the first “magic” angle.