Bistritzer-MacDonald dynamics in twisted bilayer graphene

TL;DR

This paper rigorously derives the Bistritzer-MacDonald model for twisted bilayer graphene, showing it accurately describes electron dynamics near the first magic angle based on physical parameters.

Contribution

It provides a rigorous derivation of the BM model from a tight-binding framework, clarifying the conditions under which it accurately captures electron behavior in TBG.

Findings

BM model emerges as effective dynamics for wave-packets at Dirac points

The regime where BM model applies is consistent with physical constants at the first magic angle

Error estimates for the approximation are rigorously established.

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 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.