论文标题
几何和拓扑探戈在有序和无定形的手性质中
Geometry and Topology Tango in Ordered and Amorphous Chiral Matter
论文作者
论文摘要
与从弹性组件组装的机械结构和光子超材料组装的机械结构一样多样化，具有常见的几何特征：Sublattice对称性。该特性最初引入了一种手性对称性，以表征其能量差距附近的许多电子绝缘体。在本文中，我们介绍了一个通用框架，以阐明和设计所有享受手性对称性的系统中的零能量拓扑边界模式，无论是结晶还是无定形。我们首先通过一个真实的度量来展示如何将手性绝缘子彼此区分：它们的手性极化。在晶体中，我们使用它来重新定义散装对应关系的概念，并在将其应用于手性绝缘体中解决了长期存在的歧义。在无定形的超材料中，我们使用它来制定通用的几何规则来定位拓扑不同的阶段，并解释如何与周期性结构相比，如何设计局部化的零模式波指南更健壮。
Systems as diverse as mechanical structures assembled from elastic components, and photonic metamaterials enjoy a common geometrical feature: a sublattice symmetry. This property realizes a chiral symmetry first introduced to characterize a number of electronic insulators in the vicinity of their energy gaps. In this article, we introduce a generic framework to elucidate and design zero-energy topological boundary modes in all systems enjoying a chiral symmetry, whether crystalline or amorphous. We first show how to distinguish chiral insulators from one another by a real-space measure: their chiral polarization. In crystals, we use it to redefine the very concept of bulk-boundary correspondence, and resolve long-standing ambiguities in its application to chiral insulators. In amorphous metamaterials, we use it to lay out generic geometrical rules to locate topologically distinct phases, and explain how to engineer localized zero-mode wave guides even more robust than in periodic structures.
