Origin and localization of topological band gaps in gyroscopic metamaterials

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.

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Cited by in corpus (7)

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• Amorphous topological matter: theory and experiment
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Topological Random Fractals
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Rayleigh waves and cyclotron surface modes of gyroscopic metamaterials
• Classifying topological floppy modes in the continuum