The Bistritzer-MacDonald (BM) model, introduced in \cite{Bistritzer2011},
attempts to capture the electronic properties of twisted bilayer graphene
(TBG), even at incommensurate twist angles, by an effective periodic model over
the bilayer moir\’e 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 the 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.
