Minimal non-abelian nodal braiding in ideal metamaterials.

Exploring new topological phases and phenomena has become a vital topic in condensed matter physics and materials sciences. Recent studies reveal that a braided colliding nodal pair can be stabilized in a multi-gap system with [Formula: see text] or [Formula: see text] symmetry. This exemplifies non-abelian topological charges beyond the scope of conventional single-gap abelian band topology. Here, we construct ideal acoustic metamaterials to realize non-abelian braiding with the fewest band nodes. By emulating the time with a sequence of acoustic samples, we experimentally observe an elegant but nontrivial nodal braiding process, including nodes creation, braiding, collision, and repulsion (i.e., impossible to annihilate), and measure the mirror eigenvalues to elucidate the braiding consequence. The latter, at the level of wavefunctions, is of prime importance since essentially braiding physics aims to entangle multi-band wavefunctions. Furthermore, we experimentally unveil the highly intricate correlation between the multi-gap edge responses and the bulk non-abelian charges. Our findings pave the way for developing non-abelian topological physics that is still in its infancy.