Photonic topological insulator induced by a dislocation in three dimensions.

The hallmark of topological insulators (TIs) is the scatter-free propagation of waves in topologically protected edge channels1. This transport is strictly chiral on the outer edge of the medium and therefore capable of bypassing sharp corners and imperfections, even in the presence of substantial disorder. In photonics, two-dimensional (2D) topological edge states have been demonstrated on several different platforms2-4 and are emerging as a promising tool for robust lasers5, quantum devices6-8 and other applications. More recently, 3D TIs were demonstrated in microwaves9 and  acoustic waves10-13, where the topological protection in the latter  is induced by dislocations. However, at optical frequencies, 3D photonic TIs have so far remained out of experimental reach. Here we demonstrate a photonic TI with protected topological surface states in three dimensions. The topological protection is enabled by a screw dislocation. For this purpose, we use the concept of synthetic dimensions14-17 in a 2D photonic waveguide array18 by introducing a further modal dimension to transform the system into a 3D topological system. The lattice dislocation endows the system with edge states propagating along 3D trajectories, with topological protection akin to strong photonic TIs19,20. Our work paves the way for utilizing 3D topology in photonic science and technology.

Realization of a three-dimensional photonic topological insulator.

Confining photons in a finite volume is highly desirable in modern photonic devices, such as waveguides, lasers and cavities. Decades ago, this motivated the study and application of photonic crystals, which have a photonic bandgap that forbids light propagation in all directions1-3. Recently, inspired by the discoveries of topological insulators4,5, the confinement of photons with topological protection has been demonstrated in two-dimensional (2D) photonic structures known as photonic topological insulators6-8, with promising applications in topological lasers9,10 and robust optical delay lines11. However, a fully three-dimensional (3D) topological photonic bandgap has not been achieved. Here we experimentally demonstrate a 3D photonic topological insulator with an extremely wide (more than 25 per cent bandwidth) 3D topological bandgap. The composite material (metallic patterns on printed circuit boards) consists of split-ring resonators (classical electromagnetic artificial atoms) with strong magneto-electric coupling and behaves like a 'weak' topological insulator (that is, with an even number of surface Dirac cones), or a stack of 2D quantum spin Hall insulators. Using direct field measurements, we map out both the gapped bulk band structure and the Dirac-like dispersion of the photonic surface states, and demonstrate robust photonic propagation along a non-planar surface. Our work extends the family of 3D topological insulators from fermions to bosons and paves the way for applications in topological photonic cavities, circuits and lasers in 3D geometries.

Photonic Floquet Skin-Topological Effect.

Non-Hermitian skin effect and photonic topological edge states are of great interest in non-Hermitian physics and optics. However, the interplay between them is largely unexplored. Here, we propose and demonstrate experimentally the non-Hermitian skin effect constructed from the nonreciprocal flow of Floquet topological edge states, which can be dubbed "Floquet skin-topological effect." We first show the non-Hermitian skin effect can be induced by structured loss when the one-dimensional (1D) system is periodically driven. Next, based on a two-dimensional (2D) Floquet topological photonic lattice with structured loss, we investigate the interaction between the non-Hermiticity and the topological edge states. We observe that all the one-way edge states are imposed onto specific corners, featuring both the non-Hermitian skin effect and topological edge states. Furthermore, a topological switch for the skin-topological effect is presented by utilizing the phase-transition mechanism. Our experiment paves the way for realizing non-Hermitian topological effects in nonlinear and quantum regimes.

Weyl points in a magnetic tetrahedral photonic crystal.

Weyl points have recently been predicted and experimentally observed in double-gyroid photonic crystals, as well as in other complex photonic structures such as stacked hexagonal-lattice slabs and helical waveguide arrays. In all above structures, the Weyl points are located between high frequency bands, and are difficult to probe experimentally. In this work, we show that a photonic crystal with a simple tetrahedral structure can host frequency-isolated Weyl points between the second and third bands. The minimal number of two Weyl points emerges from a threefold quadratic degeneracy at the Brillouin zone corner when time-reversal symmetry is broken. We verify theoretically that the Weyl points carry opposite topological charges, and are associated with Fermi arc-like surface states. This photonic crystal can be realized using ferromagnetic rods in the microwave frequency regime, providing a simple platform for studying the physics of Weyl points.

Weyl points in a magnetic tetrahedral photonic crystal: erratum.

We present an erratum regarding the number of space group in our paper.

Strain-Induced Gauge Field and Landau Levels in Acoustic Structures.

The emerging field of topological acoustics that explores novel gauge-field-related phenomena for sound has drawn attention in recent years. However, previous approaches constructing a synthetic gauge field for sound predominantly relied on a periodic system, being unable to form a uniform effective magnetic field, thus lacking access to some typical magnetic-induced quantum phenomena such as Landau energy quantization. Here we introduce strain engineering, previously developed in graphene electronics and later transferred to photonics, into a two-dimensional acoustic structure in order to form a uniform effective magnetic field for airborne acoustic wave propagation. Landau levels in the energy spectrum can be formed near the Dirac cone region. We also propose an experimentally feasible scheme to verify the existence of acoustic Landau levels with an acoustic measurement. As a new freedom of constructing a synthetic gauge field for sound, our study offers a path to previously inaccessible magneticlike effects in traditional periodic acoustic structures.

Acoustic Type-II Weyl Nodes from Stacking Dimerized Chains.

Lorentz-violating type-II Weyl fermions, which were missed in Weyl's prediction of nowadays classified type-I Weyl fermions in quantum field theory, have recently been proposed in condensed matter systems. The semimetals hosting type-II Weyl fermions offer a rare platform for realizing many exotic physical phenomena that are different from type-I Weyl systems. Here we construct the acoustic version of a type-II Weyl Hamiltonian by stacking one-dimensional dimerized chains of acoustic resonators. This acoustic type-II Weyl system exhibits distinct features in a finite density of states and unique transport properties of Fermi-arc-like surface states. In a certain momentum space direction, the velocity of these surface states is determined by the tilting direction of the type-II Weyl nodes rather than the chirality dictated by the Chern number. Our study also provides an approach of constructing acoustic topological phases at different dimensions with the same building blocks.

Dispersion-tunable designer-plasmonic resonator with enhanced high-order resonances.

We propose and experimentally demonstrate an approach to efficiently tune the dispersion of a designer-plasmonic resonator, or a plasmonic 'meta-atom', by incorporating an extra ground plane underneath. We demonstrate that this ground plane is able to enhance resonances, and the enhancing effect can render those higher-order azimuthal modes, being absent in previously reported designer-plasmonic resonators, experimentally observable. After incorporating the ground plane, all resonance modes are red shifted with their Q factors enhanced. By increasing the separation from the planar resonator to the underneath ground plane, all enhanced modes are blue shifted with Q factors decreased slightly, whose trend is opposite to increasing the thickness of a dielectric substrate of a common meta-atom without a ground. These results may find potential applications in tunable designer-plasmonic sensors and plasmonic metamaterial designs.

Topological acoustics.

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.

Observation of the geometry-dependent skin effect and dynamical degeneracy splitting.

The non-Hermitian skin effect is a distinctive phenomenon in non-Hermitian systems, which manifests as the anomalous localization of bulk states at the boundary. To understand the physical origin of the non-Hermitian skin effect, a bulk band characterization based on the dynamical degeneracy on an equal frequency contour is proposed, which reflects the strong anisotropy of the spectral function. In this paper, we report the experimental observation of a newly-discovered geometry-dependent non-Hermitian skin effect and dynamical degeneracy splitting in a two-dimensional acoustic crystal and reveal their remarkable correspondence by performing single-frequency excitation measurements. Our work not only provides a controllable experimental platform for studying the non-Hermitian physics, but also confirms the unique correspondence between the non-Hermitian skin effect and the dynamical degeneracy splitting, paving a new way to characterize the non-Hermitian skin effect.

Topologically crafted spatiotemporal vortices in acoustics.

Vortices in fluids and gases have piqued the human interest for centuries. Development of classical-wave physics and quantum mechanics highlighted wave vortices characterized by phase singularities and topological charges. In particular, vortex beams have found numerous applications in modern optics and other areas. Recently, optical spatiotemporal vortex states exhibiting the phase singularity both in space and time have been described. Here, we report the topologically robust generation of acoustic spatiotemporal vortex pulses. We utilize an acoustic meta-grating with broken mirror symmetry which exhibits a topological phase transition with a pair of phase singularities with opposite topological charges emerging in the momentum-frequency domain. We show that these vortices are topologically robust against structural perturbations of the meta-grating and can be employed for the generation of spatiotemporal vortex pulses. Our work paves the way for studies and applications of spatiotemporal structured waves in acoustics and other wave systems.

Fractal photonic topological insulators.

Topological insulators constitute a newly characterized state of matter that contains scatter-free edge states surrounding an insulating bulk. Conventional wisdom regards the insulating bulk as essential, because the invariants that describe the topological properties of the system are defined therein. Here, we study fractal topological insulators based on exact fractals composed exclusively of edge sites. We present experimental proof that, despite the lack of bulk bands, photonic lattices of helical waveguides support topologically protected chiral edge states. We show that light transport in our topological fractal system features increased velocities compared with the corresponding honeycomb lattice. By going beyond the confines of the bulk-boundary correspondence, our findings pave the way toward an expanded perception of topological insulators and open a new chapter of topological fractals.

Photonic Floquet topological insulators in a fractal lattice.

We present Floquet fractal topological insulators: photonic topological insulators in a fractal-dimensional lattice consisting of helical waveguides. The helical modulation induces an artificial gauge field and leads to a trivial-to-topological phase transition. The quasi-energy spectrum shows the existence of topological edge states corresponding to real-space Chern number 1. We study the propagation of light along the outer edges of the fractal lattice and find that wavepackets move along the edges without penetrating into the bulk or backscattering even in the presence of disorder. In a similar vein, we find that the inner edges of the fractal lattice also exhibit robust transport when the fractal is of sufficiently high generation. Finally, we find topological edge states that span the circumference of a hybrid half-fractal, half-honeycomb lattice, passing from the edge of the honeycomb lattice to the edge of the fractal structure virtually without scattering, despite the transition from two dimensions to a fractal dimension. Our system offers a realizable experimental platform to study topological fractals and provides new directions for exploring topological physics.

Splashing transients of 2D plasmons launched by swift electrons.

Launching of plasmons by swift electrons has long been used in electron energy-loss spectroscopy (EELS) to investigate the plasmonic properties of ultrathin, or two-dimensional (2D), electron systems. However, the question of how a swift electron generates plasmons in space and time has never been answered. We address this issue by calculating and demonstrating the spatial-temporal dynamics of 2D plasmon generation in graphene. We predict a jet-like rise of excessive charge concentration that delays the generation of 2D plasmons in EELS, exhibiting an analog to the hydrodynamic Rayleigh jet in a splashing phenomenon before the launching of ripples. The photon radiation, analogous to the splashing sound, accompanies the plasmon emission and can be understood as being shaken off by the Rayleigh jet-like charge concentration. Considering this newly revealed process, we argue that previous estimates on the yields of graphene plasmons in EELS need to be reevaluated.

Topological water wave states in a one-dimensional structure.

Topological concepts have been introduced into electronic, photonic, and phononic systems, but have not been studied in surface-water-wave systems. Here we study a one-dimensional periodic resonant surface-water-wave system and demonstrate its topological transition. By selecting three different water depths, we can construct different types of water waves - shallow, intermediate and deep water waves. The periodic surface-water-wave system consists of an array of cylindrical water tanks connected with narrow water channels. As the width of connecting channel varies, the band diagram undergoes a topological transition which can be further characterized by Zak phase. This topological transition holds true for shallow, intermediate and deep water waves. However, the interface state at the boundary separating two topologically distinct arrays of water tanks can exhibit different bands for shallow, intermediate and deep water waves. Our work studies for the first time topological properties of water wave systems, and paves the way to potential management of water waves.

Probing topological protection using a designer surface plasmon structure.

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.