Vortex states in an acoustic Weyl crystal with a topological lattice defect

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.

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.

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.

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.

Topological sound in two dimensions

Topology is the branch of mathematics studying the properties of an object that are preserved under continuous deformations. Quite remarkably, the powerful theoretical tools of topology have been applied over the past few years to study the electronic band structure of crystals. Topological band theory can explain and predict topological phase transitions in a material, and the unusual robustness of certain band structure shapes, such as Dirac cones, against small perturbations. These findings have also unveiled a new phase of matter-topological insulators-whose exotic transport properties at their boundaries are topologically protected against imperfections and disorder. The fascinating features of topological boundary states have triggered the search for their analogs in classical wave physics. Here, we focus on the peculiar features of two-dimensional topological insulators for sound and mechanical waves. Two-dimensional Dirac cones and phononic topological insulators can emerge under certain conditions in periodic acoustic metamaterials, demonstrating great potential for acoustic and mechanical systems to demonstrate, over a tabletop platform, complex fundamental phenomena driven by topological concepts. In addition, these discoveries offer a direct path toward new technologies for enhanced sound control and manipulation.

Bound vortex light in an emulated topological defect in photonic lattices

Topology have prevailed in a variety of branches of physics. And topological defects in cosmology are speculated akin to dislocation or disclination in solids or liquid crystals. With the development of classical and quantum simulation, such speculative topological defects are well-emulated in a variety of condensed matter systems. Especially, the underlying theoretical foundations can be extensively applied to realize novel optical applications. Here, with the aid of transformation optics, we experimentally demonstrated bound vortex light on optical chips by simulating gauge fields of topological linear defects in cosmology through position-dependent coupling coefficients in a deformed photonic graphene. Furthermore, these types of photonic lattices inspired by topological linear defects can simultaneously generate and transport optical vortices, and even can control the orbital angular momentum of photons on integrated optical chips.

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

Building upon the bulk-boundary correspondence in topological phases of matter, disclinations have recently been harnessed to trap fractionally quantized density of states (DOS) in classical wave systems. While these fractional DOS have associated states localized to the disclination's core, such states are not protected from deconfinement due to the breaking of chiral symmetry, generally leading to resonances which, even in principle, have finite lifetimes and suboptimal confinement. Here, we devise and experimentally validate in acoustic lattices a paradigm by which topological states bind to disclinations without a fractional DOS but which preserve chiral symmetry. The preservation of chiral symmetry pins the states at the midgap, resulting in their protected maximal confinement. The integer DOS at the defect results in twofold degenerate states that, due to symmetry constraints, do not gap out. Our study provides a fresh perspective about the interplay between symmetry protection in topological phases and topological defects, with possible applications in classical and quantum systems alike.

Progress in Topological Mechanics

Topological mechanics is rapidly emerging as an attractive field of research where mechanical waveguides can be designed and controlled via topological methods. With the development of topological phases of matter, recent advances have shown that topological states have been realized in the elastic media exploiting analogue quantum Hall effect, analogue quantum spin Hall effect, analogue quantum valley Hall effect, higher-order topological physics, topological pump, topological lattice defects and so on. This review aims to introduce the experimental and theoretical achievements with defect-immune protected elastic waves in mechanical systems based on the abovementioned methods, respectively. From these discussions, we predict the possible perspective of topological mechanics.

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.

Observation of Dislocation-Induced Topological Modes in a Three-Dimensional Acoustic Topological Insulator

The interplay between real-space topological lattice defects and the reciprocal-space topology of energy bands can give rise to novel phenomena, such as one-dimensional topological modes bound to screw dislocations in three-dimensional topological insulators. We obtain direct experimental observations of dislocation-induced helical modes in an acoustic analog of a weak three-dimensional topological insulator. The spatial distribution of the helical modes is found through spin-resolved field mapping, and verified numerically by tight-binding and finite-element calculations. These one-dimensional helical channels can serve as robust waveguides in three-dimensional media. Our experiment paves the way to studying novel physical modes and functionalities enabled by topological lattice defects in three-dimensional classical topological materials.

Frequency manipulation of topological surface states by Weyl phase transitions

By creating a synthetic frequency dimension with dynamic modulation in a 2D honeycomb waveguide array, we construct both Type-I and Type-II Weyl semimetals (WSMs) and utilize the WSM phase transition to control the frequency evolutions of topological surface states. We show that Type-I WSMs and Type-II WSMs manifest opposite and same band slopes for the two surface states, which give rise to the bidirectional and unidirectional frequency shifts, respectively. Moreover, by cascading Type-I Weyl lattices and Type-II Weyl lattices together, we also achieve the time-reversed evolution of frequency, such as frequency negative refraction, bandwidth expansion-compression, and perfect imaging. The Letter may find applications in robust signal transmission and processing with synthesized topological states.

Acoustic Bessel Vortex Beam by Quasi-Three-Dimensional Reflected Metasurfaces

Vortex beams have a typical characteristic of orbital angular momentum, which provides a new degree of freedom for information processing in remote communication and a form of non-contact manipulation for trapping particles. In acoustics, vortex beams are generally observed on the surface of a metamaterial structure or in a waveguide with a hard boundary owing to the characteristic of easy diffusion in free space. The realization of an acoustic vortex beam with a long-distance propagation in free space still remains a challenge. To overcome this, we report a type of acoustic Bessel vortex (ABV) beam created by a quasi-three-dimensional reflected metasurface in free space based on phase modulation. By using the Bessel and vortex phase profiles, we can realize an ABV beam with the high performances of both Bessel and vortex beams, and its effective propagation distance is larger than 9.2λ in free space. Beyond that, we discuss the bandwidth and topological charge of the ABV beam in detail, and the fractional bandwidth can reach about 0.28. The proposed ABV beam has the advantages of a high-performance vortex, long-distance propagation, and broad bandwidth, which provide a new pathway for designing multifunctional vortex devices with promising applications.