Discovery of Higher-Order Nodal Surface Semimetals.

The emergent higher-order topological insulators significantly deepen our understanding of topological physics. Recently, the study has been extended to topological semimetals featuring gapless bulk band nodes. To date, higher-order nodal point and line semimetals have been successfully realized in different physical platforms. However, for the conceptually expected higher-order nodal surface semimetals, a concrete model has yet to be proposed, let alone experimentally observed. Here, we report an ingenious design route for constructing this unprecedented higher-order topological phase. The three-dimensional model, layer-stacked with a two-dimensional anisotropic Su-Schrieffer-Heeger lattice, exhibits appealing hinge arcs connecting the projected nodal surfaces. Experimentally, we realize this new topological phase in an acoustic metamaterial, and present unambiguous evidence for both the bulk nodal structure and hinge arc states, the two key manifestations of the higher-order nodal surface semimetal. Our findings can be extended to other classical systems such as photonic, elastic, and electric circuit systems, and open new possibilities for controlling waves.

Topological negative refraction of surface acoustic waves in a Weyl phononic crystal.

Reflection and refraction of waves occur at the interface between two different media. These two fundamental interfacial wave phenomena form the basis of fabricating various wave components, such as optical lenses. Classical refraction-now referred to as positive refraction-causes the transmitted wave to appear on the opposite side of the interface normal compared to the incident wave. By contrast, negative refraction results in the transmitted wave emerging on the same side of the interface normal. It has been observed in artificial materials1-5, following its theoretical prediction6, and has stimulated many applications including super-resolution imaging7. In general, reflection is inevitable during the refraction process, but this is often undesirable in designing wave functional devices. Here we report negative refraction of topological surface waves hosted by a Weyl phononic crystal-an acoustic analogue of the recently discovered Weyl semimetals8-12. The interfaces at which this topological negative refraction occurs are one-dimensional edges separating different facets of the crystal. By tailoring the surface terminations of the Weyl phononic crystal, constant-frequency contours of surface acoustic waves can be designed to produce negative refraction at certain interfaces, while positive refraction is realized at different interfaces within the same sample. In contrast to the more familiar behaviour of waves at interfaces, unwanted reflection can be prevented in our crystal, owing to the open nature of the constant-frequency contours, which is a hallmark of the topologically protected  surface states in Weyl crystals8-12.

Universal Mirror-Stacking Approach for Constructing Topological Bound States in the Continuum.

Bound states in the continuum (BICs) are counterintuitive localized states with eigenvalues embedded in the continuum of extended states. Recently, nontrivial band topology is exploited to enrich the BIC physics, resulting in topological BICs (TBICs) with extraordinary robustness against perturbations or disorders. Here, we propose a simple but universal mirror-stacking approach to turn nontrivial bound states of any topological monolayer model into TBICs. Physically, the mirror-stacked bilayer Hamiltonian can be decoupled into two independent subspaces of opposite mirror parities, each of which directly inherits the energy spectrum information and band topology of the original monolayer. By tuning the interlayer couplings, the topological bound state of one subspace can move into and out of the continuum of the other subspace continuously without hybridization. As representative examples, we construct one-dimensional first-order and two-dimensional higher-order TBICs, and demonstrate them unambiguously by acoustic experiments. Our findings will expand the research implications of both topological materials and BICs.

Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions.

Topological features embedded in ancient braiding and knotting arts endow significant impacts on our daily life and even cutting-edge science. Recently, fast growing efforts are invested to the braiding topology of complex Bloch bands in non-Hermitian systems. This new classification of band topology goes far beyond those established in Hermitian counterparts. Here, we present the first acoustic realization of the topological non-Hermitian Bloch braids, based on a two-band model easily accessible for realizing any desired knot structure. The non-Hermitian bands are synthesized by a simple binary cavity-tube system, where the long-range, complex-valued, and momentum-resolved couplings are accomplished by a well-controlled unidirectional coupler. In addition to directly visualizing various two-band braiding patterns, we unambiguously observe the highly elusive topological phase transitions between them. Not only do our results provide a direct demonstration for the non-Hermitian band topology, but also the experimental techniques open new avenues for designing unconventional acoustic metamaterials.

Tracking Valley Topology with Synthetic Weyl Paths.

Inspired by the newly emergent valleytronics, great interest has been attracted to the topological valley transport in classical metacrystals. The presence of nontrivial domain-wall states is interpreted with a concept of valley Chern number, which is well defined only in the limit of small band gap. Here, we propose a new visual angle to track the intricate valley topology in classical systems. Benefiting from the controllability of our acoustic metacrystals, we construct Weyl points in synthetic three-dimensional momentum space through introducing an extra structural parameter (rotation angle here). As such, the two-dimensional valley-projected band topology can be tracked with the strictly quantized topological charge in three-dimensional Weyl crystal, which features open surface arcs connecting the synthetic Weyl points and gapless chiral surface states along specific Weyl paths. All theoretical predictions are conclusively identified by our acoustic experiments. Our findings may promote the development of topological valley physics, which is less well defined yet under hot debate in multiple physical disciplines.

Acoustic Realization of Surface-Obstructed Topological Insulators.

Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without bulk closure and exhibits as an obstruction of higher-dimensional boundary states. Here, we report the first experimental realization of three-dimensional surface-obstructed topological insulators with using acoustic crystals. Our acoustic measurements demonstrate unambiguously the emergence of one-dimensional topological hinge states in the middle of the bulk and surface band gaps, as a direct manifestation of the higher-order band topology. Together with comparative measurements for the trivial and phase-transition-point insulators, our experimental data conclusively evidence the unique bulk-boundary physics for the surface-obstructed band topology. That is, the topological phase transition is determined by the closure of the surface gap, rather than by closing the bulk gap. Our study might spur on new activities to deepen the understanding of such elusive topological phases.

Acoustic Möbius Insulators from Projective Symmetry.

In the presence of gauge symmetry, common but not limited to artificial crystals, the algebraic structure of crystalline symmetries needs to be projectively represented, giving rise to unprecedented topological physics. Here, we demonstrate this novel idea by exploiting a projective translation symmetry and constructing a variety of Möbius-twisted topological phases. Experimentally, we realize two Möbius insulators in acoustic crystals for the first time: a two-dimensional one of first-order band topology and a three-dimensional one of higher-order band topology. We observe unambiguously the peculiar Möbius edge and hinge states via real-space visualization of their localiztions, momentum-space spectroscopy of their 4π periodicity, and phase-space winding of their projective translation eigenvalues. Not only does our work open a new avenue for artificial systems under the interplay between gauge and crystalline symmetries, but it also initializes a new framework for topological physics from projective symmetry.

Higher-Order Dirac Sonic Crystals.

Discovering new topological phases of matter is a major theme in fundamental physics and materials science. Dirac semimetal provides an exceptional platform for exploring topological phase transitions under symmetry breaking. Recent theoretical studies have revealed that a three-dimensional Dirac semimetal can harbor fascinating hinge states, a higher-order topological manifestation not known before. However, its realization in experiment is yet to be achieved. In this Letter, we propose a minimum model to construct a spinless higher-order Dirac semimetal protected by C_{6v} symmetry. By breaking different symmetries, this parent phase transitions into a variety of novel topological phases including higher-order topological insulator, higher-order Weyl semimetal, and higher-order nodal-ring semimetal. Furthermore, for the first time, we experimentally realize this unprecedented higher-order topological phase in a sonic crystal and present an unambiguous observation of the desired hinge states via momentum-space spectroscopy and real-space visualization. Our findings may offer new opportunities to manipulate classical waves such as sound and light.

Acoustic Realization of Quadrupole Topological Insulators.

A quadrupole topological insulator, being one higher-order topological insulator with nontrivial quadrupole quantization, has been intensely investigated very recently. However, the tight-binding model proposed for such emergent topological insulators demands both positive and negative hopping coefficients, which imposes an obstacle in practical realizations. Here, we introduce a feasible approach to design the sign of hopping in acoustics, and construct the first acoustic quadrupole topological insulator that stringently emulates the tight-binding model. The inherent hierarchy quadrupole topology has been experimentally confirmed by detecting the acoustic responses at the bulk, edge, and corner of the sample. Potential applications can be anticipated for the topologically robust in-gap states, such as acoustic sensing and energy trapping.

Probing Weyl Physics with One-Dimensional Sonic Crystals.

Recently, intense efforts have been devoted to realizing classical analogues of various topological phases of matter. In this Letter, we explore the intriguing Weyl physics by a simple one-dimensional sonic crystal, in which two extra structural parameters are combined to construct a synthetic three-dimensional space. Based on our ultrasonic experiments, we have not only observed the synthetic Weyl points, but also probed the novel reflection phase singularity that connects inherently with the topological robustness of Weyl points. The presence of topologically nontrivial interface modes has been demonstrated further. As the first realization of topological acoustics in synthetic space, our study exhibits great potential of probing high-dimensional topological phenomena by such easily fabricated and detected low-dimension acoustic systems.

Valley Topological Phases in Bilayer Sonic Crystals.

Recently, the topological physics in artificial crystals for classical waves has become an emerging research area. In this Letter, we propose a unique bilayer design of sonic crystals that are constructed by two layers of coupled hexagonal array of triangular scatterers. Assisted by the additional layer degree of freedom, a rich topological phase diagram is achieved by simply rotating scatterers in both layers. Under a unified theoretical framework, two kinds of valley-projected topological acoustic insulators are distinguished analytically, i.e., the layer-mixed and layer-polarized topological valley Hall phases, respectively. The theory is evidently confirmed by our numerical and experimental observations of the nontrivial edge states that propagate along the interfaces separating different topological phases. Various applications such as sound communications in integrated devices can be anticipated by the intriguing acoustic edge states enriched by the layer information.

Valley Vortex States in Sonic Crystals.

Valleytronics is quickly emerging as an exciting field in fundamental and applied research. In this Letter, we study the acoustic version of valley states in sonic crystals and reveal a vortex nature of such states. In addition to the selection rules established for exciting valley polarized states, a mimicked valley Hall effect of sound is proposed further. The extraordinary chirality of valley vortex states, detectable in experiments, may open a new possibility in sound manipulations. This is appealing to scalar acoustics that lacks a spin degree of freedom inherently. In addition, the valley selection enables a handy way to create vortex matter in acoustics, in which the vortex chirality can be controlled flexibly. Potential applications can be anticipated with the exotic interaction of acoustic vortices with matter, such as to trigger the rotation of the trapped microparticles without contact.

Construction and Observation of Flexibly Controllable High-Dimensional Non-Hermitian Skin Effects.

Non-Hermitian skin effect (NHSE) is one of the most fundamental phenomena in non-Hermitian physics. It is established that 1D NHSE originates from the nontrivial spectral winding topology. However, the topological origin behind the higher-dimensional NHSE remains unclear, which poses a substantial challenge in constructing and manipulating high-dimensional NHSEs. Here, an intuitive bottom-to-top scheme to construct high-dimensional NHSEs is proposed, through assembling multiple independent 1D NHSEs. Not only the elusive high-dimensional NHSEs can be effectively predicted from the well-defined 1D spectral winding topologies, but also the high-dimensional generalized Brillouin zones can be directly synthesized from the 1D counterparts. As examples, two 2D nonreciprocal acoustic metamaterials are experimentally implemented to demonstrate highly controllable multi-polar NHSEs and hybrid skin-topological effects, where the sound fields can be frequency-selectively localized at any desired corners and boundaries. These results offer a practicable strategy for engineering high-dimensional NHSEs, which can boost advanced applications such as selective filters and directional amplifiers.

Minimal non-abelian nodal braiding in ideal metamaterials.

Exploring new topological phases and phenomena has become a vital topic in condensed matter physics and materials sciences. Recent studies reveal that a braided colliding nodal pair can be stabilized in a multi-gap system with [Formula: see text] or [Formula: see text] symmetry. This exemplifies non-abelian topological charges beyond the scope of conventional single-gap abelian band topology. Here, we construct ideal acoustic metamaterials to realize non-abelian braiding with the fewest band nodes. By emulating the time with a sequence of acoustic samples, we experimentally observe an elegant but nontrivial nodal braiding process, including nodes creation, braiding, collision, and repulsion (i.e., impossible to annihilate), and measure the mirror eigenvalues to elucidate the braiding consequence. The latter, at the level of wavefunctions, is of prime importance since essentially braiding physics aims to entangle multi-band wavefunctions. Furthermore, we experimentally unveil the highly intricate correlation between the multi-gap edge responses and the bulk non-abelian charges. Our findings pave the way for developing non-abelian topological physics that is still in its infancy.

Superconducting characteristics of 4-A carbon nanotube-zeolite composite.

We have fabricated nanocomposites consisting of 4-A carbon nanotubes embedded in the 0.7-nm pores of aluminophosphate-five (AFI) zeolite that display a superconducting specific heat transition at 15 K. MicroRaman spectra of the samples show strong and spatially uniform radial breathing mode (RBM) signals at 510 cm(-1) and 550 cm(-1), characteristic of the (4, 2) and (5, 0) nanotubes, respectively. The specific heat transition is suppressed at >2 T, with a temperature dependence characteristic of finite-size effects. Comparison with theory shows the behavior to be consistent with that of a type II BCS superconductor, characterized by a coherence length of 14 +/- 2 nm and a magnetic penetration length of 1.5 +/- 0.7 mum. Four probe and differential resistance measurements have also indicated a superconducting transition initiating at 15 K, but the magnetoresistance data indicate the superconducting network to be inhomogeneous, with a component being susceptible to magnetic fields below 3 T and other parts capable of withstanding a magnetic field of 5 T or beyond.

Topological dislocation modes in three-dimensional acoustic topological insulators.

Dislocations are ubiquitous in three-dimensional solid-state materials. The interplay of such real space topology with the emergent band topology defined in reciprocal space gives rise to gapless helical modes bound to the line defects. This is known as bulk-dislocation correspondence, in contrast to the conventional bulk-boundary correspondence featuring topological states at boundaries. However, to date rare compelling experimental evidences have been presented for this intriguing topological observable in solid-state systems, owing to the huge challenges in creating controllable dislocations and conclusively identifying topological signals. Here, using a three-dimensional acoustic weak topological insulator with precisely controllable dislocations, we report an unambiguous experimental evidence for the long-desired bulk-dislocation correspondence, through directly measuring the gapless dispersion of the one-dimensional topological dislocation modes. Remarkably, as revealed in our further experiments, the pseudospin-locked dislocation modes can be unidirectionally guided in an arbitrarily-shaped dislocation path. The peculiar topological dislocation transport, expected in a variety of classical wave systems, can provide unprecedented control over wave propagations.

Resonant terahertz transmissions through metal hole array on silicon substrate.

We have observed resonant terahertz transmission peaks in samples comprising perforated periodic hole array in a metal film, covered with a high dielectric substrate. These resonant transmissions arise from the interplay between waveguide modes in dielectric substrate and the periodic hole array in the metal film. Finite difference time domain (FDTD) simulations show good agreement with the data, in support of the proposed mechanism. Inducing additional resonant transmissions using guided modes can lead to the ease in tuning the transmission peak frequencies that are potentially useful to terahertz (THz) bio-sensing.

Acoustic transmission enhancement through a periodically structured stiff plate without any opening.

We report both experimentally and theoretically that enhanced acoustic transmission can occur in the subwavelength region through a thin but stiff structured plate without any opening. This exotic acoustic phenomenon is essentially distinct from the previous related studies originated from, either collectively or individually, the interaction of the incident wave with openings in previous structures. It is attributed to the structure-induced resonant excitation of the nonleaky Lamb modes that exist intrinsically in the uniform elastic plate. Our finding should have an impact on ultrasonic applications.

Valley-locked waveguide transport in acoustic heterostructures.

Valley pseudospin, labeling the pair of energy extrema in momentum space, has been attracting attention because of its potential as a new degree of freedom in manipulating electrons or classical waves. Recently, topological valley edge transport of sound, by virtue of the gapless valley-locked edge states, has been observed in the domain walls of sonic crystals. Here, by constructing a heterostructure with sonic crystals, a topological waveguide is realized. The waveguide states feature gapless dispersion, momentum-valley locking, immunity against defects, and a high capacity for energy transport. With a designable size, the heterostructures are more flexible for interfacing with the existing acoustic devices than the domain wall structures. Such heterostructures may serve as versatile new devices for acoustic wave manipulation, such as acoustic splitting, reflection-free guiding and converging.

Observation of quadratic Weyl points and double-helicoid arcs.

Novel quasiparticles beyond those mimicking the elementary high-energy particles such as Dirac and Weyl fermions have attracted great interest in condensed-matter physics and materials science. Here we report an experimental observation of the long-desired quadratic Weyl points by using a three-dimensional chiral metacrystal of sound waves. Markedly different from the newly observed unconventional quasiparticles, such as the spin-1 Weyl points and the charge-2 Dirac points featuring respectively threefold and fourfold band crossings, the charge-2 Weyl points identified here are simply twofold degenerate, and the dispersions around them are quadratic in two directions and linear in the third one. Besides the essential nonlinear bulk dispersions, we further unveil the exotic double-helicoid surface arcs that emanate from a projected quadratic Weyl point and terminate at two projected conventional Weyl points. This unique global surface connectivity provides conclusive evidence for the double topological charges of such unconventional topological nodes.