Discovery of topological metamaterials by symmetry relaxation and smooth topological indicators

TL;DR

This paper introduces a method to identify and design topological metamaterials by breaking symmetries to make topological indices smoothly variable, enabling efficient optimization and discovery of new topological phases.

Contribution

It proposes a novel approach that relaxes symmetry constraints to allow gradient-based design of topological materials, including phononic systems with higher-order topological insulators.

Findings

Successfully designed phononic topological insulators using the new method

Demonstrated the approach on both discrete and continuous systems

Enabled efficient optimization of topological properties through symmetry relaxation

Abstract

Robustness against small perturbations is a crucial feature of topological properties. This robustness is both a source of theoretical interest and a drive for technological applications, but presents a challenge when looking for new topological systems: Small perturbations cannot be used to identify the global direction of change in the topological indices. Here, we overcome this limitation by breaking the symmetries protecting the topology. The introduction of symmetry-breaking terms causes the topological indices to become non-quantized variables, which are amenable to efficient design algorithms based on gradient methods. We demonstrate this capability by designing discrete and continuous phononic systems realizing conventional and higher-order topological insulators.