论文标题
局部缺陷模式的渐近表征：Su-Schrieffer-Heeger和相关模型
Asymptotic characterisation of localised defect modes: Su-Schrieffer-Heeger and related models
论文作者
论文摘要
在波浪物理学中受拓扑保护状态的动机，我们研究了具有缺陷的一维周期培养基中的局部本征模。 Su-Schrieffer-Heeger模型（具有拓扑保护的局部缺陷状态的一维系统的规范示例）用于演示该方法。我们的方法可用于描述两个广泛的扰动类别，以解决周期性的差异问题：插入有限尺寸的任意材料以及通过在两个不同的周期性媒体之间创建接口引起的材料引起的。此处介绍的结果表征了每种情况下局部本本码的存在，并且在存在时确定其本征频率，并提供简明的分析结果，以量化这些模式的衰减率。这些结果是使用高频均质化和转移矩阵分析获得的，两种方法之间具有良好的一致性。
Motivated by topologically protected states in wave physics, we study localised eigenmodes in one-dimensional periodic media with defects. The Su-Schrieffer-Heeger model (the canonical example of a one-dimensional system with topologically protected localised defect states) is used to demonstrate the method. Our approach can be used to describe two broad classes of perturbations to periodic differential problems: those caused by inserting a finite-sized piece of arbitrary material and those caused by creating an interface between two different periodic media. The results presented here characterise the existence of localised eigenmodes in each case and, when they exist, determine their eigenfrequencies and provide concise analytic results that quantify the decay rate of these modes. These results are obtained using both high-frequency homogenisation and transfer matrix analysis, with good agreement between the two methods.
