Dynamics of Self-Dual Kagome Metamaterials and the Emergence of Fragile Topology

Pegah Azizi, Siddhartha Sarkar, Kai Sun, Stefano Gonella

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Abstract

Recent years have seen the discovery of systems featuring fragile topological states. These states of matter lack certain protection attributes typically associated with topology and are therefore characterized by weaker signatures that make them elusive to observe. Moreover, they are typically confined to special symmetry classes and, in general, rarely studied in the context of phononic media. In this Letter, we theoretically predict the emergence of fragile topological bands in the spectrum of a twisted kagome elastic lattice with threefold rotational symmetry, in the so-called self-dual configuration. A necessary requirement is that the lattice is a structural metamaterial, in which the role of the hinges is played by elastic finite-thickness ligaments. The interplay between the edge modes appearing in the band gaps bounding the fragile topological states is also responsible for the emergence of corner modes at selected corners of a finite hexagonal domain, which qualifies the lattice as a second-order topological insulator. We demonstrate our findings through a series of experiments via 3D scanning laser doppler vibrometry conducted on a physical prototype. The selected configuration stands out for its remarkable geometric simplicity and ease of physical implementation in the panorama of dynamical systems exhibiting fragile topology.

Original languageEnglish (US)
Article number156101
JournalPhysical review letters
Volume130
Issue number15
DOIs
StatePublished - Apr 14 2023

Bibliographical note

Funding Information:
P. A. acknowledges support of the UMN CSE Graduate Fellowship. S. G. acknowledges support from the National Science Foundation (Grant No. CMMI-2027000). S. S. and K. S. acknowledge support from the Office of Naval Research (Grant No. MURI N00014-20-1-2479).

Publisher Copyright:
© 2023 American Physical Society.

PubMed: MeSH publication types

  • Journal Article

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