Bistritzer-MacDonald dynamics in twisted bilayer graphene
arXiv:2207.13767 · doi:10.1063/5.0115771
Abstract
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 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 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.
arXiv comment50 pages, 9 figures. Fixed wave-packet scaling, bounded some higher-order terms in the residual, and added reference to Bal-Cazeaux-Massatt-Quinn. Bounding the higher-order terms required strengthening our assumption on the regularity of initial data
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