Minimal non-abelian nodal braiding in ideal metamaterials

Abstract

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 $$PT$$ P T or $${C}_{2z}T$$ C 2 z T 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.

Topological phononic metamaterials

“…The earring nodal links were verified experimentally in band dispersions at different frequencies by performing three-dimensional Fourier transforms of the scanned fields. Later, Qiu et al realized the similar nontrivial non-Abelian braiding process of band nodes in acoustic metamaterials based on a square lattice model [433]. However, taking a step forward, they provided the first experimental evidence of the stability of pair nodes of non-Abelian charges (see figure 31(d)).…”

“…For instance, the phonon spectra in layered silicates were predicted to host the non-Abelian physics [422]. By far, thanks to the designability of artificial materials, the non-Abelian band topology has been proposed, manipulated, and probed in various metamaterials such as transmission line networks [416,432], phononic crystals [53,433,434] full-dielectric [435] and biaxial photonic crystals [432,[436][437][438][439] and spring-mass systems [440]. Among them, the first direct observation of the non-Abelian topological charges was achieved by Guo et al [416] in a one-dimensional PT-symmetric three-band insulator system using transmission line network metamaterials.…”

“…Many topological phenomena are discovered/observed first in phononic metamaterials. For instance, topological negative refraction [47], topological sasers [48], pseudospin-and valleypolarized edge states [209,219], higher-order topological insulators [51,52,78,84], higher-order Weyl semimetal phases [318,319], Dirac vortex states [217], topological Wannier cycles [49], spectral flows in fragile topological insulators [719], non-Abelian braiding of band nodes [53,433,434], non-Hermitian morphing of topological modes [628,720], and topological exceptional nexus [721] were first discovered in phononic metamaterials.…”

Floquet non-Abelian topological insulator and multifold bulk-edge correspondence

“…For instance, in the presence of space-time inversion (PT) symmetry, onedimensional (1D) insulators involving multiple bandgaps may carry non-Abelian quaternion charges 8 and host richer topological phases as experimentally observed in transmission line networks 16,17 . Yet in its infancy, the tangled multi-gap topology plays a vital role in describing, e.g., the disclination defects of nematic liquids [18][19][20][21][22] , the admissible nodal lines [23][24][25][26][27] , and the reciprocal braiding of Dirac/Weyl/exceptional points 11,[28][29][30][31] .…”