Singular Topological Edge States in Locally Resonant Metamaterials

TL;DR

This paper demonstrates the emergence of topological edge states within local resonance-induced bandgaps in metamaterials, combining theoretical modeling and experimental validation to extend the scope of topological metamaterials.

Contribution

It introduces a model showing topological edge states within local resonance bandgaps by achieving simultaneous topological phase and bandgap transitions.

Findings

Topological edge states can exist within local resonance bandgaps.

Experimental evidence shows distinct wave localization in topological modes.

The study extends the understanding of topological effects in resonant metamaterials.

Abstract

Band topology has emerged as a novel tool for material design across various domains, including photonic and phononic systems, and metamaterials. A prominent model for band topology is the Su-Schrieffer-Heeger (SSH) chain, which reveals topological in-gap states within Bragg-type gaps (BG) formed by periodic modification. Apart from classical BGs, another mechanism for bandgap formation in metamaterials involves strong coupling between local resonances and propagating waves, resulting in a local resonance-induced bandgap (LRG). Previous studies have shown the challenge of topological edge state emergence within the LRG. Here, we reveal that topological edge states can emerge within an LRG by achieving both topological phase and bandgap transitions simultaneously. We describe this using a model of inversion-symmetric extended SSH chains for locally resonant metamaterials. Notably, this topological state can lead to highly localized modes, comparable to a subwavelength unit cell, when it emerges within the LRG. We experimentally demonstrate distinct differences in topologically protected modes -- highlighted by wave localization -- between the BG and the LRG using locally resonant granule-based metamaterials. Our findings suggest the scope of topological metamaterials may be extended via their bandgap nature.