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Non-Abelian topological insulators have been realized on transmission lines and acoustic systems, whereas their implementation at optical frequencies remains elusive. Here, the authors propose a minimal model for non-Abelian topological insulators and experimentally demonstrate a six-band system in a photonic waveguide array, at around 800 nm.

Non-Abelian topological charges and edge states in a PT-symmetric transmission line network are experimentally observed, and a non-Abelian quotient relation for the bulk–edge correspondence is found.

Bulk and edge modes and their relation in topological materials is something researchers have been tried to harness for various applications. Here the authors provide a method to achieve chiral anomaly bulk states by applying boundary conditions to a topologically trivial crystal.

Fluid-solid interaction, long investigated, is mostly neglected in topological acoustics. Here the authors find that it can give rise to intriguing topological phenomena in simple phononic crystals due to intrinsic differences between sound in fluid and solid.

A characteristic feature of non-Hermitian systems is an exceptional point at which eigenvalues and eigenstates coalesce. They also support richer degeneracies—a swallowtail catastrophe—that reveals transitions among three different types of singularity.

Hybrid skin-topological effect (HSTE) is a new phenomenon involving the interplay between non-Hermitian skin effects and topological edge states. Here, the authors highlight the key role of boundary configurations and experimentally observe HSTE states using synthetic complex frequencies.

Realization of a gyromagnetic double-zero-index metamaterial results in unconventional optical and topological properties, suitable to be used for the generation of light pulses shaped as a vortex both in time and space.

In optics, schemes have been proposed to realize synthetic gauge fields, but are restricted to the Abelian type. Here, the authors demonstrate synthetic SU(2) non-Abelian gauge fields in anisotropic media, which allows the study of novel optical phenomena not found in Abelian synthetic gauge field systems.

Employing connected coaxial waveguides on a nested meta-crystal configuration, the authors design photonic crystals with scalar-wave-like band dispersions, facilitating the search for topological phases in three-dimensional photonic crystals.

The appearance of toroidal multipolar moments in electrodynamics interrogates the question for their existence in Berry curvature, which can be seen as the “magnetic field” in the momentum space. Here, the authors observe 3D vortex distributions in the Berry curvature within a photonic metamaterial.

A 2D Dirac cone photonic system with inhomogeneous effective mass gives rise to an in-plane synthetic magnetic field, inducing chiral zeroth Landau levels with one-way propagative characteristics.

Non-Abelian topological insulators receive increasing attention due to entangled bulk bandgaps different from Abelian counterparts. Here, the authors realize two new classes of topological charges characterizing of a four-band non-Abelian topological insulator.

Although it shows promise for applications, non-Abelian braiding is difficult to realize in electronic systems. Its demonstration using acoustic waveguides may provide a useful platform to study non-Abelian physics.

Non-Hermitian physics expands the range of exotic features that can be explored in non-trivial topological systems and exceptional points play a prominent role. Here, the authors report a topological classification of the intersections of exceptional surfaces and predicted topologically protected edge states that arise from the intersections.

Exceptional points are of great importance to rationalize the topological properties of non-Hermitian systems. This study proposes a new class of non-Hermitian topological degeneracies named exceptional chains, and develops a general theory to understand such non-Hermitian crystalline system by merging non-Hermitian and topological fields.

Exceptional degeneracies in non-Hermitian systems give rise to distinctive phenomena like bulk-Fermi-arcs. In this work, the authors present an unconventional bulk-Fermi-arc that links third-order exceptional points, experimentally demonstrated using topological circuits, with potential applications in wave manipulation.