标题： 调制超材料中的边缘模式基于三间隙定理 显示英文标题

标题： Edge modes in modulated metamaterials based on the three-gap theorem

摘要： 我们提出了一种新的生成复杂结构材料的范式，该范式基于三间隙定理，统一并推广了研究局域边缘态中的几个关键概念。 我们的模型既有SSH模型的离散耦合强度，还有一个调制参数，可用于表征边缘模的谱流，并产生类似于霍夫施塔特蝴蝶的图像。 通过为每个本征模定义一个局域化因子，我们能够建立有限系统中局域边缘态存在的条件。 这使我们能够将它们的本征频率与相应无限周期问题的谱进行比较，并表征随着我们三间隙算法参数变化时出现和消失（在成为非局域化的意义上）的丰富局域边缘模模式。 显示英文摘要

摘要： We present a new paradigm for generating complex structured materials based on the three-gap theorem that unifies and generalises several key concepts in the study of localised edge states. Our model has both the discretised coupling strengths of the SSH model and a modulation parameter that can be used to characterise the spectral flow of edge modes and produce images reminiscent of the Hofstadter butterfly. By defining a localisation factor associated to each eigenmode, we are able to establish conditions for the existence of localised edge states in finite systems. This allows us to compare their eigenfrequencies with the spectra of the corresponding infinitely periodic problem and characterise the rich pattern of localised edge modes appearing and disappearing (in the sense of becoming delocalised) as the parameters of our three-gap algorithm are varied.