Origin and localization of topological band gaps in gyroscopic metamaterials

TL;DR

This paper investigates how topological band gaps in gyroscopic metamaterials can arise independently of periodic order, introducing a local feature-based method for predicting topological phases and revealing disorder-induced topological transitions.

Contribution

It presents a novel local-feature-based approach to predict topological gaps and Chern numbers, and demonstrates that amorphous gyroscopic systems can exhibit topological phases similar to ordered lattices.

Findings

Topological gaps can form without periodic order.

A local method predicts topological phases efficiently.

Disorder can induce topological phase transitions.

Abstract

Networks of interacting gyroscopes have proven to be versatile structures for understanding and harnessing finite-frequency topological excitations. Spinning components give rise to band gaps and topologically protected wave transport along the system's boundaries, whether the gyroscopes are arranged in a lattice or in an amorphous configuration. Here, we examine the irrelevance of periodic order for generating topological gaps. Starting from the symplectic dynamics of our model metamaterial, we present a general method for predicting whether a gap exists and for approximating the Chern number using only local features of a network, bypassing the costly diagonalization of the system's dynamical matrix. We then study how strong disorder interacts with band topology in gyroscopic metamaterials and find that amorphous gyroscopic Chern insulators exhibit similar critical behavior to periodic lattices. Our experiments and simulations additionally reveal a topological Anderson insulation transition, wherein disorder drives a trivial phase into a topological one.