The manipulation of acoustic wave propagation in fluids has numerous applications, including some in everyday life. Acoustic technologies frequently develop in tandem with optics, using shared concepts such as waveguiding and metamedia. It is thus noteworthy that an entirely novel class of electromagnetic waves, known as "topological edge states," has recently been demonstrated. These are inspired by the electronic edge states occurring in topological insulators, and possess a striking and technologically promising property: the ability to travel in a single direction along a surface without backscattering, regardless of the existence of defects or disorder. Here, we develop an analogous theory of topological fluid acoustics, and propose a scheme for realizing topological edge states in an acoustic structure containing circulating fluids. The phenomenon of disorder-free one-way sound propagation, which does not occur in ordinary acoustic devices, may have novel applications for acoustic isolators, modulators, and transducers.

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Recently discovered1,2 valley photonic crystals (VPCs) mimic many of the unusual properties of two-dimensional (2D) gapped valleytronic materials [3][4][5][6][7][8][9] . Of the utmost interest to optical communications is their ability to support topologically protected chiral edge (kink) states [3][4][5][6][7][8][9] at the internal domain wall between two VPCs with opposite valley-Chern indices. Here we experimentally demonstrate valley-polarized kink states with polarization multiplexing in VPCs, designed from a spin-compatible four-band model. When the valley pseudospin is conserved, we show that the kink states exhibit nearly perfect out-coupling e ciency into directional beams, through the intersection between the internal domain wall and the external edge separating the VPCs from ambient space. The out-coupling behaviour remains topologically protected even when we break the spin-like polarization degree of freedom (DOF), by introducing an e ective spin-orbit coupling in one of the VPC domains. This also constitutes the first realization of spin-valley locking for topological valley transport.

We report the first experimental realization of a three-dimensional thermal cloak shielding an air bubble in a bulk metal without disturbing the external conductive thermal flux. The cloak is made of a thin layer of homogeneous and isotropic material with specially designed three-dimensional manufacturing. The cloak's thickness is 100  μm while the cloaked air bubble has a diameter of 1 cm, achieving the ratio between dimensions of the cloak and the cloaked object 2 orders smaller than previous thermal cloaks, which were mainly realized in a two-dimensional geometry. This work can find applications in novel thermal devices in the three-dimensional physical space.

Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths. However, the intrinsic difference between electrons and photons determines that the ‘topological protection' in time-reversal-invariant photonic systems does not share the same robustness as its counterpart in electronic topological insulators. Here in a designer surface plasmon platform consisting of tunable metallic sub-wavelength structures, we construct photonic topological edge states and probe their robustness against a variety of defect classes, including some common time-reversal-invariant photonic defects that can break the topological protection, but do not exist in electronic topological insulators. This is also an experimental realization of anomalous Floquet topological edge states, whose topological phase cannot be predicted by the usual Chern number topological invariants.

Recent theories have proposed a concept of valley photonic crystals as an analog of gapped valleytronic materials such as MoS 2 and bilayer graphene. Here, we further extend the applicability of valley photonic crystals to surface electromagnetic waves and experimentally demonstrate a valley surface-wave photonic crystal on a single metal surface as a photonic duplicate of MoS 2 . Both bulk transport and edge transport are directly mapped with a near-field microwave imaging system. The photonic valley pseudospins are demonstrated, together with the photonic valley Hall effect that splits the opposite photonic valley pseudospins into two opposite directions. The valley edge transport in MoS 2 or other transition-metal dichalcogenide monolayers, which is different from bilayer graphene but still stays unrealized in condensed-matter systems, is demonstrated on this MoS 2 -like photonic platform. Our study not only offers a tabletop platform to study the valleytronic physics, but also opens a venue for on-chip integrated photonic device applications using valley-polarized information.

The recent discovery of higher-order topological insulators (TIs) [1-5] has opened new possibilities in the search for novel topological materials and metamaterials. Secondorder TIs have been implemented in two-dimensional (2D) systems [6-19] exhibiting topological 'corner states', as well as three-dimensional (3D) systems having one-dimensional (1D) topological 'hinge states' [20]. Third-order TIs, which have topological states three dimensions lower than the bulk (which must thus be 3D or higher), have not yet been reported. Here, we describe the realization of a third-order TI in an anisotropic diamondlattice acoustic metamaterial. The bulk acoustic bandstructure has nontrivial topology characterized by quantized Wannier centers. By direct acoustic measurement, we observe corner states at two corners of a rhombohedron-like structure, as predicted by the quantized Wannier centers. This work extends topological corner states from 2D to 3D, and may find applications in novel acoustic devices.Higher-order TIs are a new class of topological materials supporting a generalization of the bulk-boundary correspondence principle, in which topological states are guaranteed to exist along boundaries two or more dimensions smaller than that of the bulk [1][2][3][4][5]. In standard TIs, topological edge states occur at one lower dimension than the bulk [21,22]; for instance, a quantum Hall insulator has a 2D bulk and topological states on 1D edges. By contrast, a 2D second-order TI supports zero-dimensional (0D) topological 'corner states'. Such a lattice was first devised based on quantized quadrupole moments [1,2] and quickly realized in mechanical [6], electromagnetic [7], and electrical [9] metamaterials. Later, another type of 2D second-order TIs based on quantized Wannier centers, was proposed [23][24][25] and demonstrated in acoustic metamaterials [10,11]. In 3D materials, second-order TI behavior has also been observed in the form of 1D topological 'hinge states' in bismuth [20].According to theoretical predictions, TIs of arbitrarily high order are possible. However, in real materials the bulk is at most 3D. Thus, barring the use of 'synthetic' dimensions [26,27], the only remaining class of high-order TI is a third-order TI with 3D bulk and 0D corner states.As of this writing, no such material has been reported in the literature, although there exists a theoretical proposal based on quantized octupole moments [1,2].Here, we realize a third-order TI in a 3D acoustic metamaterial, observing topological states at the corners of a rhombohedron-like sample. This third-order TI is based on the extension of Wannier-type second-order TIs to 3D [23,25], and can be regarded as a 3D generalization of the classic 1D Su-Schrieffer-Heeger (SSH) model [28]. Just as in the SSH case, the eigenmode polarizations are quantized by lattice symmetries, and the Wannier centers are pinned to highsymmetry points; the mismatch between the Wannier centers and lattice truncations gives rise to charge fractionalization and hence lower-dimensio...

Revealing how 2D plasmons emerge and evolve in electron energy–loss spectroscopy (EELS).