We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the incommensurability of the layers. The Bistritzer-MacDonald PDE model, which is periodic with respect to the bilayer's moir\'e pattern, has recently been shown to rigorously describe these dynamics in a parameter regime. In this work, we first prove that the dynamics of the tight-binding model of incommensurate twisted bilayer graphene can be approximated by computations on finite domains. The main ingredient of this proof is a speed of propagation estimate proved using Combes-Thomas estimates. We then provide extensive numerical computations which clarify the range of validity of the Bistritzer-MacDonald model.

翻译：我们考虑了在扭曲双层石墨烯中数值计算电子量子动力学的问题。挑战在于由于层间的非公度性，原子尺度的动力学模型在一般扭曲角度下是非周期的。Bistritzer-MacDonald偏微分方程模型以双层莫尔条纹图案为周期，近期已被严格证明可在特定参数区间内描述这些动力学。本文首先证明，非公度扭曲双层石墨烯紧束缚模型的动力学可通过有限域上的计算进行近似。该证明的主要工具是基于Combes-Thomas估计的传播速度估计。随后我们通过大量数值计算，阐明了Bistritzer-MacDonald模型的适用范围。