Minimal non-abelian nodal braiding in ideal metamaterials

TL;DR

This paper demonstrates the experimental realization of non-abelian nodal braiding in ideal acoustic metamaterials, revealing complex topological phenomena and their implications for future non-abelian topological physics.

Contribution

It constructs minimal acoustic metamaterials to observe and analyze non-abelian braiding of band nodes, including creation, braiding, and collision processes.

Findings

Experimental observation of non-abelian nodal braiding

Measurement of mirror eigenvalues to confirm braiding

Correlation between edge responses and bulk non-abelian charges

Abstract

Exploring new topological phases and phenomena has become a vital topic in condensed matter physics and material sciences. It is generally believed that a pair of band nodes with opposite topological charges will annihilate after collision. Recent studies reveal that a braided colliding nodal pair can be stabilized in a multi-gap system with PT or C_2z T symmetry. Beyond the conventional single-gap abelian band topology, this intriguing phenomenon exemplifies non-abelian topological charges. Here, we construct ideal acoustic metamaterials to realize non-abelian braiding with the fewest band nodes. We experimentally observe an elegant but nontrivial nodal braiding process, including nodes creation, braiding, collision, and repulsion (i.e., failure to annihilate), and measure the mirror eigenvalues to elucidate the essential braiding consequence. The latter, at the level of wavefunctions, is of prime importance since the braiding physics essentially aims to entangle multi-band wavefunctions. Furthermore, we experimentally unveil the highly intricate correspondence between the edge responses and the bulk non-abelian charges. Notably, all our experimental data perfectly reproduce our numerical simulations. Our findings pave the way for developing non-abelian topological physics that is still in its infancy.