Exploring photonic topology: Scattering topological effects are being explored in a variety of electronic and optical materials systems owing to their robustness against defects (see the Perspective by Özdemir). Yang et al. designed and fabricated an ideal optical analog of a three-dimensional Weyl system. Angular transmission measurements revealed four Weyl points at the same energy, as well as the signature helicoidal arcs associated with such an exotic topological system. Zhou et al. theoretically proposed and experimentally demonstrated the formation of a topologically protected bulk Fermi arc. They attributed the formation of the arc to the topological nature of paired exceptional points (points at which gain and loss in the system are matched). Photonic crystals may provide a powerful platform for studying exotic properties of topological electronic systems and may also be used to develop optical devices that exploit topological properties of light-matter interactions. Science , this issue p. 1013 , p. 1009 ; see also p. 995

Non-Abelian phenomena arise when the sequence of operations on physical systems influences their behaviors. By possessing internal degrees of freedom such as polarization, light and sound can be subjected to various manipulations, including constituent materials, structured environments, and tailored source conditions. These manipulations enable the creation of a great variety of Hamiltonians, through which rich non-Abelian phenomena can be explored and observed. Recent developments have constituted a versatile testbed for exploring non-Abelian physics at the intersection of atomic, molecular, and optical physics; condensed matter physics; and mathematical physics. These fundamental endeavors could enable photonic and acoustic devices with multiplexing functionalities. Our review aims to provide a timely and comprehensive account of this emerging topic. Starting from the foundation of matrix-valued geometric phases, we address non-Abelian topological charges, non-Abelian gauge fields, non-Abelian braiding, non-Hermitian non-Abelian phenomena, and their realizations with photonics and acoustics and conclude with future prospects.

In crystals, two bands may cross each other and form degeneracies along a closed loop in the three-dimensional momentum space, which is called nodal line. Nodal line degeneracy can be designed to exhibit various configurations such as nodal rings, chains, links, and knots. Very recently, non-Abelian band topology was proposed in nodal link systems, where the nodal lines formed by consecutive pairs of bands exhibit interesting braiding structures and the underlying topological charges are described by quaternions. Here, we experimentally demonstrate non-Abelian nodal links in a biaxial hyperbolic metamaterial. The linked nodal lines threading through each other are formed by the crossings between three adjacent bands. Based on the non-Abelian charges, we further analyze various admissible nodal link configurations for the three-band system. On the interface between the metamaterial and air, surface bound states in the continuum are observed, which serves as the symmetry-enforced derivative of drumhead surface states from the linked nodal lines. Our work serves as a direct observation of the global topological structures of nodal links, and provides a platform for studying non-Abelian topological charge in the momentum space.

Weyl points are discrete locations in the three-dimensional momentum space where two bands cross linearly with each other. They serve as the monopoles of Berry curvature in the momentum space, and their existence requires breaking of either time-reversal or inversion symmetry^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}. Although various non-centrosymmetric Weyl systems have been reported¹⁵, demonstration of Weyl degeneracies due to breaking of the time-reversal symmetry remains scarce and is limited to electronic systems^17,18. Here, we report the experimental observation of photonic Weyl degeneracies in a magnetized semiconductor—InSb, which behaves as a magnetized plasma¹⁹ for electromagnetic waves at the terahertz band. By varying the magnetic field strength, Weyl points and the corresponding photonic Fermi arcs have been demonstrated. Our observation establishes magnetized semiconductors as a reconfigurable²⁰ terahertz Weyl system, which may prompt research on novel magnetic topological phenomena such as chiral Majorana-type edge states and zero modes in classic systems^21,22.

Topology in higher dimensions: In condensed-matter systems, the band structure of a material has often been equated with functionality. However, consideration of the topology of the band structure now provides a route to develop a functionality that goes far beyond the expected properties of the materials. Using electromagnetic metamaterials as building blocks, Ma et al . realized a five-dimensional generalization of a topological Weyl semimetal. Along with the three real momentum dimensions, these included two bi-anisotropy material parameters as synthetic dimensions to demonstrate both linked Weyl surfaces and Yang monopoles. The metamaterial platform provides a powerful route to explore the exotic physics associated with higher-order topological phenomena. —ISO