标题： 高阶连续体模型用于扭曲双层石墨烯 显示英文标题

标题： Higher-order continuum models for twisted bilayer graphene

摘要： 由Bistritzer和MacDonald提出的首阶连续体PDE模型\cite{bistritzer2011moire}准确描述了在小扭曲角度下扭曲双层石墨烯（TBG）的单粒子电子性质。 在本文中，我们通过系统的多尺度展开获得了Bistritzer-MacDonald模型的高阶修正。 我们证明，在自然参数选择和给定初始条件（这些初始条件在单层狄拉克点上谱局部化）下，所得高阶PDE模型的解准确地近似了相应的紧束缚波函数。 紧束缚和连续体动力学的数值模拟验证了高阶连续体模型的有效性。 还讨论了高阶模型的对称性。 这项工作扩展了从\cite{watson2023bistritzer}的分析，该分析严格建立了（一阶）BM模型的有效性。 显示英文摘要

摘要： 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.