Topological Edge Modes by Smart Patterning

TL;DR

This paper introduces a new approach to creating topological edge modes in meta-materials through specific patterning of resonators, enabling scalable and practical topological devices.

Contribution

It defines and proves the concept of topological patterns in resonator arrays using $K$-theory and demonstrates a novel experimental platform with magnetically coupled spinners.

Findings

Topological patterns ensure boundary modes fill spectral gaps.

The approach is independent of resonator structure and coupling details.

Practical platform allows scalable topological meta-materials.

Abstract

The research in topological materials and meta-materials reached maturity and is now gradually entering the phase of practical applications and devices. However, scaling down the experimental demonstrations definitely presents a challenge. In this work, we study coupled identical resonators whose collective dynamics is fully determined by the pattern in which the resonators are arranged. We call a pattern topological if boundary resonant modes fully fill all existing spectral gaps whenever the pattern is halved. This is a characteristic of the pattern and is entirely independent of the structure of the resonators and the details of the couplings. Existence of such patterns is proven using $K$-theory and exemplified using a novel experimental platform based on magnetically coupled spinners. Topological meta-materials built on these principles can be easily engineered at any scale, providing a practical platform for applications and devices.