Higher-order continuum models for twisted bilayer graphene
Abstract
The first-order continuum PDE model proposed by Bistritzer and MacDonald in \cite{bistritzer2011moire} accurately describes the single-particle electronic properties of twisted bilayer graphene (TBG) at small twist angles. In this paper, we obtain higher-order corrections to the Bistritzer-MacDonald model via a systematic multiple-scales expansion. We prove that the solution of the resulting higher-order PDE model 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. Numerical simulations of tight-binding and continuum dynamics demonstrate the validity of the higher-order continuum model. Symmetries of the higher-order models are also discussed. This work extends the analysis from \cite{watson2023bistritzer}, which rigorously established the validity of the (first-order) BM model.
Cite
@article{arxiv.2502.08120,
title = {Higher-order continuum models for twisted bilayer graphene},
author = {Solomon Quinn and Tianyu Kong and Mitchell Luskin and Alexander B. Watson},
journal= {arXiv preprint arXiv:2502.08120},
year = {2025}
}