We employed ab initio calculations to identify a class of crystalline materials of $M\mathrm{Si}$ ($M=\mathrm{Fe}$, Co, Mn, Re, Ru) having double-Weyl points in both their acoustic and optical phonon spectra. They exhibit novel topological points termed “spin-1 Weyl point” at the Brillouin zone center and “charge-2 Dirac point” at the zone corner. The corresponding gapless surface phonon dispersions are two helicoidal sheets whose isofrequency contours form a single noncontractible loop in the surface Brillouin zone. In addition, the global structure of the surface bands can be analytically expressed as double-periodic Weierstrass elliptic functions.

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

The vortex, a fundamental topological excitation featuring the in-plane winding of a vector field, is important in various areas such as fluid dynamics, liquid crystals, and superconductors. Although commonly existing in nature, vortices were observed exclusively in real space. Here, we experimentally observed momentum-space vortices as the winding of far-field polarization vectors in the first Brillouin zone of periodic plasmonic structures. Using homemade polarization-resolved momentum-space imaging spectroscopy, we mapped out the dispersion, lifetime, and polarization of all radiative states at the visible wavelengths. The momentum-space vortices were experimentally identified by their winding patterns in the polarization-resolved isofrequency contours and their diverging radiative quality factors. Such polarization vortices can exist robustly on any periodic systems of vectorial fields, while they are not captured by the existing topological band theory developed for scalar fields. Our work provides a new way for designing high-$Q$ plasmonic resonances, generating vector beams, and studying topological photonics in the momentum space.

On-site nano-kirigami enabled continuous shape transformation of gold nanofilm for 3D nanofabrication and giant optical chirality.