Dynamics of self-dual kagome metamaterials and the emergence of fragile topology

TL;DR

This paper predicts and demonstrates the emergence of fragile topological states in a self-dual twisted kagome elastic lattice, revealing second-order topological insulator behavior through experiments on a physical prototype.

Contribution

It introduces a simple, experimentally realizable elastic metamaterial exhibiting fragile topological bands and second-order topological insulator features.

Findings

Fragile topological bands are predicted in a self-dual kagome lattice.

Edge modes lead to corner modes, indicating second-order topology.

Experimental validation via laser vibrometry confirms theoretical predictions.

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 three-fold 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 bandgaps 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.