Bistritzer-MacDonald dynamics in twisted bilayer graphene

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.

50 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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Cited by in corpus (7)

• A simple derivation of moiré-scale continuous models for twisted bilayer graphene
• Flat Bands and High Chern Numbers in Twisted Multilayer Graphene
• Diagrammatic perturbation approach to moiré bands in twisted bilayer graphene
• Exact ground state of interacting electrons in magic angle graphene
• Classically forbidden regions in the chiral model of twisted bilayer graphene. With an appendix by Zhongkai Tao and Maciej Zworski
• Magic distances in twisted bilayer graphene
• Incommensurate Twisted Bilayer Graphene: emerging quasi-periodicity and stability