Modeling of Electronic Dynamics in Twisted Bilayer Graphene

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-05-14 DOI:10.1137/23m1595941

Tianyu Kong, Diyi Liu, Mitchell Luskin, Alexander B. Watson

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1011-1038, June 2024.
Abstract. 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 moiré 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.

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扭曲双层石墨烯电子动力学建模

SIAM 应用数学杂志》，第 84 卷第 3 期，第 1011-1038 页，2024 年 6 月。摘要。我们考虑的问题是如何数值计算电子在扭曲双层石墨烯中的量子动力学。面临的挑战是，由于各层的不可比性，原子尺度的动力学模型在一般扭曲角度下是非周期性的。Bistritzer-MacDonald PDE 模型相对于双层石墨烯的摩尔纹是周期性的，最近的研究表明，该模型能在参数机制中严格描述这些动力学。在这项工作中，我们首先证明了不可通约扭曲双层石墨烯紧密结合模型的动力学可以通过有限域上的计算来近似。该证明的主要内容是利用康伯斯-托马斯估计值证明的传播速度估计值。然后，我们提供了大量数值计算，澄清了 Bistritzer-MacDonald 模型的有效范围。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.