Observation of Degenerate Zero-Energy Topological States at Disclinations in an Acoustic Lattice

Topological acoustofluidics

The complex interaction of spin, valley and lattice degrees of freedom allows natural materials to create exotic topological phenomena. The interplay between topological wave materials and hydrodynamics could offer promising opportunities for visualizing topological physics and manipulating bioparticle unconventionally. Here we present topological acoustofluidic chips to illustrate the complex interaction between elastic valley spin and nonlinear fluid dynamics. We created valley streaming vortices and chiral swirling patterns for backward-immune particle transport. Using tracer particles, we observed arrays of clockwise and anticlockwise valley vortices due to an increase in elastic spin density. Moreover, we discovered exotic topological pressure wells in fluids, creating nanoscale trapping fields for manipulating DNA molecules. We also found a 93.2% modulation in the bandwidth of edge states, dependent on the orientation of the substrate's crystallographic structure. Our study sets the stage for uncovering topological acoustofluidic phenomena and visualizing elastic valley spin, revealing the potential for topological-material applications in life sciences.

A new class of higher-order topological insulators that localize energy at arbitrary multiple sites

Z-classified topological phases lead to a larger-than-unity number of topological states. However, these multiple topological states are only localized at the corners in nonlocal systems. Here, first, we rigorously prove that the multiple topological states of nonlocal Su-Schrieffer-Heeger (SSH) chains can be inherited and realized by local aperiodic chains with only the nearest couplings. Then, we report a new class of higher-order topological insulators constructed with the local aperiodic chains, which can have any integer number of 0D topological states localized at arbitrary positions in the whole domain of the insulators, including within the bulk. The 0D topological states are protected by the local topological marker in each direction, instead of the bulk multipole chiral numbers in existing work. We experimentally demonstrate these multimode topological states in designed acoustic coupled-resonators systems. Our work enables multiple combinations of localized corner-bulk topological states, which leads to programmable lasers and sasers by selecting the excitation sites without altering the structure, and thus opens a new avenue to signal enhancement for computing and sensing.

Topological Disclination States and Charge Fractionalization in a Non-Hermitian Lattice

We show that a non-Hermitian lattice with a disclination can host topological disclination states that are induced by on-site gain and loss. The disclination states are inherently non-Hermitian as they do not exist in the limit of zero gain or loss. They arise from charge fractionalization in the non-Hermitian lattice, which we establish using non-Hermitian Wilson loops calculated with biorthogonal products. The model is suitable for realization on established experimental platforms, such as arrays of photonic or polaritonic resonators. The emergence of the topological disclination states can manifest as an abrupt shift in emission intensity and frequency with varying gain or loss.

Topological orbital angular momentum extraction and twofold protection of vortex transport

Vortex phenomena are ubiquitous in nature. In optics, despite the availability of numerous techniques for vortex generation and detection, topological protection of vortex transport with desired orbital angular momentum (OAM) remains a challenge. Here, by use of topological disclination, we demonstrate a scheme to confine and guide vortices featuring arbitrary high-order charges. Such a scheme relies on twofold topological protection: a non-trivial winding in momentum space due to chiral symmetry, and a non-trivial winding in real space due to the complex coupling of OAM modes across the disclination structure. We unveil a vorticity-coordinated rotational symmetry, which sets up a universal relation between the vortex topological charge and the rotational symmetry order of the system. As an example, we construct photonic disclination lattices with a single core but different C n symmetries and achieve robust transport of an optical vortex with preserved OAM solely corresponding to one selected zero-energy vortex mode at the mid-gap. Furthermore, we show that such topological structures can be used for vortex filtering to extract a chosen OAM mode from mixed excitations. Our results illustrate the fundamental interplay of vorticity, disclination and higher-order topology, which may open a new pathway for the development of OAM-based photonic devices such as vortex guides, fibres and lasers.

Vortex solitons in topological disclination lattices

The existence of thresholdless vortex solitons trapped at the core of disclination lattices that realize higher-order topological insulators is reported. The study demonstrates the interplay between nonlinearity and higher-order topology in these systems, as the vortex state in the disclination lattice bifurcates from its linear topological counterpart, while the position of its propagation constant within the bandgap and localization can be controlled by its power. It is shown that vortex solitons are characterized by strong field confinement at the disclination core due to their topological nature, leading to enhanced stability. Simultaneously, the global discrete rotational symmetry of the disclination lattice imposes restrictions on the maximal possible topological charge of such vortex solitons. The results illustrate the strong stabilizing action that topologically nontrivial structures may exert on excited soliton states, opening new prospects for soliton-related applications.

Observation of a Photonic Orbital Gauge Field

Gauge field is widely studied in natural and artificial materials. With an effective magnetic field for uncharged particles, many intriguing phenomena are observed in several systems like photonic Floquet topological insulator. However, previous researches about the gauge field mostly focus on limited dimensions such as the Dirac spinor in graphene materials. Here, an orbital gauge field based on photonic triangular lattices is first proposed and experimentally observed. Disclination defects with Frank angle Ω created on such lattices breaks the original lattice symmetry and generates purely geometric gauge field operating on orbital basis functions. Interestingly, it is found that bound states near zero energy with the orbital angular momentum (OAM) l = 2 are intensively confined at the disclination as gradually expanding Ω. Moreover, the introduction of a vector potential field breaks the time-reversal symmetry of the orbital gauge field, experimentally manifested by the chiral transmission of light on helical waveguides. The orbital gauge field further suggests fantastic applications of manipulating the vortex light in photonic integrated devices.

Realization of a Z-Classified Chiral-Symmetric Higher-Order Topological Insulator in a Coupling-Inverted Acoustic Crystal

Higher-order topological band theory has transformed the landscape of topological phases in quantum and classical systems. Here, we experimentally demonstrate a two-dimensional higher-order topological phase, referred to as the multiple chiral topological phase, which is protected by a multipole chiral number (MCN). Our realization differs from previous higher-order topological phases in that it possesses a larger-than-unity MCN, which arises when the nearest-neighbor couplings are weaker than long-range couplings. Our phase has an MCN of 4, protecting the existence of 4 midgap topological corner modes at each corner. The multiple topological corner modes demonstrated here could lead to enhanced quantum-inspired devices for sensing and computing. Our study also highlights the rich and untapped potential of long-range coupling manipulation for future research in topological phases.

Observation of nonlinear disclination states

Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at disclinations. Appearance of these topological states is consistent with the bulk-disclination correspondence principle, and is due to the filling anomaly that results in fractional charges to the boundary unit cells. So far, topological disclination states were observed only in the linear regime, while the interplay between nonlinearity and topology in the systems with disclinations has been never studied experimentally. We report here on the experimental observation of the nonlinear photonic disclination states in waveguide arrays with pentagonal or heptagonal disclination cores inscribed in transparent optical medium using the fs-laser writing technique. The transition between nontopological and topological phases in such structures is controlled by the Kekulé distortion coefficient r with topological phase hosting simultaneously disclination states at the inner disclination core and spatially separated from them corner-I, corner-II, and extended edge states at the outer edge of the structure. We show that the robust nonlinear disclination states bifurcate from their linear counterparts and that location of their propagation constants in the gap and, hence, their spatial localization can be controlled by their power. Nonlinear disclination states can be efficiently excited by Gaussian input beams, but only if they are focused into the waveguides belonging to the disclination core, where such topological states reside. Our results open new prospects for investigation of nonlinear effects in topological systems with disclinations and are relevant for different areas of science, including Bose-Einstein and polariton condensates, where potentials with the disclinations can be created.

A second wave of topological phenomena in photonics and acoustics

Light and sound are the most ubiquitous forms of waves, associated with a variety of phenomena and physical effects such as rainbows and echoes. Light and sound, both categorized as classical waves, have lately been brought into unexpected connections with exotic topological phases of matter. We are currently witnessing the onset of a second wave of active research into this topic. The past decade has been marked by fundamental advances comprising two-dimensional quantum Hall insulators and quantum spin and valley Hall insulators, whose topological properties are characterized using linear band topology. Here, going beyond these conventional topological systems, we focus on the latest frontiers, including non-Hermitian, nonlinear and non-Abelian topology as well as topological defects, for which the characterization of the topological features goes beyond the standard band-topology language. In addition to an overview of the current state of the art, we also survey future research directions for valuable applications.

Revealing topology in metals using experimental protocols inspired by K-theory

Topological metals are conducting materials with gapless band structures and nontrivial edge-localized resonances. Their discovery has proven elusive because traditional topological classification methods require band gaps to define topological robustness. Inspired by recent theoretical developments that leverage techniques from the field of C^∗-algebras to identify topological metals, here, we directly observe topological phenomena in gapless acoustic crystals and realize a general experimental technique to demonstrate their topology. Specifically, we not only observe robust boundary-localized states in a topological acoustic metal, but also re-interpret a composite operator-mathematically derived from the K-theory of the problem-as a new Hamiltonian whose physical implementation allows us to directly observe a topological spectral flow and measure the topological invariants. Our observations and experimental protocols may offer insights for discovering topological behaviour across a wide array of artificial and natural materials that lack bulk band gaps.

Topological Metamaterials

The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

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.

Spinful Topological Phases in Acoustic Crystals with Projective PT Symmetry

For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological phases. However, only recently has it been realized theoretically that in the presence of gauge symmetry, the algebraic structure of symmetries can be projectively represented, which possibly enables the switch between spinless and spinful topological phases. Here, we report the experimental demonstration of this idea by realizing spinful topological phases in "spinless" acoustic crystals with projective space-time inversion symmetry. In particular, we realize a one-dimensional topologically gapped phase characterized by a 2Z winding number, which features double-degenerate bands in the entire Brillouin zone and two pairs of degenerate topological boundary modes. Our Letter thus overcomes a fundamental constraint on topological phases by spin classes.

A solution to the biophysical fractionation of extracellular vesicles: Acoustic Nanoscale Separation via Wave-pillar Excitation Resonance (ANSWER)

High-precision isolation of small extracellular vesicles (sEVs) from biofluids is essential toward developing next-generation liquid biopsies and regenerative therapies. However, current methods of sEV separation require specialized equipment and time-consuming protocols and have difficulties producing highly pure subpopulations of sEVs. Here, we present Acoustic Nanoscale Separation via Wave-pillar Excitation Resonance (ANSWER), which allows single-step, rapid (<10 min), high-purity (>96% small exosomes, >80% exomeres) fractionation of sEV subpopulations from biofluids without the need for any sample preprocessing. Particles are iteratively deflected in a size-selective manner via an excitation resonance. This previously unidentified phenomenon generates patterns of virtual, tunable, pillar-like acoustic field in a fluid using surface acoustic waves. Highly precise sEV fractionation without the need for sample preprocessing or complex nanofabrication methods has been demonstrated using ANSWER, showing potential as a powerful tool that will enable more in-depth studies into the complexity, heterogeneity, and functionality of sEV subpopulations.

Observation of Topological p-Orbital Disclination States in Non-Euclidean Acoustic Metamaterials

Disclinations-topological defects ubiquitously existing in various materials-can reveal the intrinsic band topology of the hosting material through the bulk-disclination correspondence. In low-dimensional materials and nanostructure such as graphene and fullerenes, disclinations yield curved surfaces and emergent non-Euclidean geometries that are crucial in understanding the properties of these materials. However, the bulk-disclination correspondence has never been studied in non-Euclidean geometry, nor in systems with p-orbital physics. Here, by creating p-orbital topological acoustic metamaterials with disclination-induced conic and hyperbolic surfaces, we demonstrate the rich emergent bound states arising from the interplay among the real-space geometry, the bulk band topology, and the p-orbital physics. This phenomenon is confirmed by clear experimental evidence that is consistent with theory and simulations. Our experiment paves the way toward topological phenomena in non-Euclidean geometries and will stimulate interesting research on, e.g., topological phenomena for electrons in nanomaterials with curved surfaces.