Amorphous topological insulators constructed from random point sets

TL;DR

This paper demonstrates that amorphous mechanical and electronic topological insulators can be constructed from arbitrary point sets, enabling robust, non-crystalline topological metamaterials with protected edge modes.

Contribution

It introduces a method to create amorphous topological insulators from various random and quasi-regular structures, expanding the design space beyond periodic lattices.

Findings

Amorphous gyroscopic networks exhibit topologically protected edge modes.

Local decoration controls the topological properties of the spectrum.

The approach is robust and applicable across scales and systems.

Abstract

The discovery that the band structure of electronic insulators may be topologically non-trivial has unveiled distinct phases of electronic matter with novel properties. Recently, mechanical lattices have been found to have similarly rich structure in their phononic excitations, giving rise to protected uni-directional edge modes whose existence was demonstrated in lattices of interacting gyroscopes and coupled pendula. In all these cases, however, as well as in other topological metamaterials, the underlying structure was finely tuned, be it through periodicity, quasi-periodicity or isostaticity. Here we show that amorphous mechanical Chern insulators consisting of interacting gyroscopes can be readily constructed from arbitrary underlying structures, including hyperuniform, jammed, quasi-crystalline, and uniformly random point sets. While our findings apply to mechanical and electronic systems alike, we focus on networks of interacting gyroscopes as a model system. Local decoration control the topology of the vibrational spectrum, endowing amorphous structures with protecting edge modes -- with a chirality of choice. Using a real-space generalization of the Chern number, we investigate the topology of our structures numerically, analytically and experimentally. The robustness of our approach enables the topological design and self-assembly of non-crystalline topological metamaterials on the micro and macro scale.