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Geometry and topology tango in ordered and amorphous chiral matter

Marcelo Guzmán, Denis Bartolo, David Carpentier

SciPost Phys. 12, 038 (2022) · published 25 January 2022


Systems as diverse as mechanical structures and photonic metamaterials enjoy a common geometrical feature: a sublattice or chiral symmetry first introduced to characterize electronic insulators. We show how a real-space observable, the chiral polarization, distinguishes chiral insulators from one another and resolve long-standing ambiguities in the very concept of their bulk-boundary correspondence. We use it to lay out generic geometrical rules to engineer topologically distinct phases, and design zero-energy topological boundary modes in both crystalline and amorphous metamaterials.

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