Non-Abelian Braiding of Topological Edge Bands

Abstract

Braiding is a geometric concept that manifests itself in a variety of scientific contexts from biology to physics, and has been employed to classify bulk band topology in topological materials. Topological edge states can also form braiding structures, as demonstrated recently in a type of topological insulators known as Möbius insulators, whose topological edge states form two braided bands exhibiting a Möbius twist. While the formation of Möbius twist is inspiring, it belongs to the simple Abelian braid group ${\mathbb{B}}_2$. The most fascinating features about topological braids rely on the non-Abelianness in the higher-order braid group ${\mathbb{B}}_N$ ($N\ge 3$), which necessitates multiple edge bands, but so far it has not been discussed. Here, based on the gauge enriched symmetry, we develop a scheme to realize non-Abelian braiding of multiple topological edge bands. We propose tight-binding models of topological insulators that are able to generate topological edge states forming non-Abelian braiding structures. Experimental demonstrations are conducted in two acoustic crystals, which carry three and four braided acoustic edge bands, respectively. The observed braiding structure can correspond to the topological winding in the complex eigenvalue space of projective translation operator, akin to the previously established point-gap winding topology in the bulk of the Hatano-Nelson model. Our work also constitutes the realization of non-Abelian braiding topology on an actual crystal platform, but not based on the "virtual" synthetic dimensions.

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Cited by in corpus (8)

• Versatile Braiding of Non-Hermitian Topological Edge States
• Observation of nonlinear higher-order topological insulators with unconventional boundary truncations
• Observation of Braid-Protected Unpaired Exceptional Points
• Brillouin Platycosms and Topological Phases
• Entanglement manifestation of knot topology in a non-Hermitian lattice
• Non-Abelian interference of topological edge states
• Exceptional topology on nonorientable manifolds
• Braiding of dynamical eigenvalues of Hermitian bosonic Kitaev chains