Higher-order corrections to the Bistritzer-MacDonald model
The first-order continuum model proposed by Bistritzer and MacDonald in 2011 accurately describes the electronic properties of twisted bilayer graphene at small twist angles. In this talk, we discuss extensions of the Bistritzer-MacDonald (BM) model to higher-order partial differential equations in the form of a systematic multiple-scales expansion. We show that the solution of these PDEs accurately approximates the corresponding tight-binding wave function under a natural choice of parameters and given initial conditions that are spectrally localized to the monolayer Dirac points. Symmetries of the higher-order models will also be discussed. This work builds on the 2023 JMP paper by Watson, Kong, MacDonald, and Luskin, which rigorously established the validity of the (first-order) BM model.