Geometry and Topology Tango in Ordered and Amorphous Chiral Matter

Abstract

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.

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• Bulk-boundary correspondence from the inter-cellular Zak phase
• Topological Weaire-Thorpe models of amorphous matter
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Cited by in corpus (12)

• Bulk-edge correspondence in the trimer Su-Schrieffer-Heeger model
• Amorphous topological matter: theory and experiment
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Breakdown of Conventional Winding Number Calculation in One-Dimensional Lattices with Interactions Beyond Nearest Neighbors
• Estimating bulk and edge topological indices in finite open chiral chains
• Bulk-boundary correspondence in extended trimer Su-Schrieffer-Heeger model
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Revealing the spatial nature of sublattice symmetry
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Topological zero-modes of the spectral localizer of trivial metals
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- part II: Higher-dimensional spectral invariants
• Topological Interface States and Nonlinear Thermoelectric Performance in Armchair Graphene Nanoribbon Heterostructures