A second wave of topological phenomena in photonics and acoustics

Pseudospin-dependent acoustic topological edge and corner states in silica aerogel metamaterialsa)

Fueled by the concepts of topological insulators, analogous topological acoustics offer an alternative approach to manipulate sound. Theoretical proposals for subwavelength acoustic topological insulators are considered to be ideal effective parameters or utilizeing artificial coiling-space metamaterials. However, the corresponding realization using realistic soft metamaterials remains challenging. In this study, we present the design of an acoustic subwavelength second-order topological insulator using nanoscale porous solid material, silica aerogel, which supports pseudospin-dependent topological edge and corner states simultaneously. Through simulations and experiments, we demonstrate that silica aerogel can function as a soft acoustic metamaterial at the subwavelength scale. By embedding silica aerogel in an air matrix to construct a honeycomb lattice, a double Dirac cone is obtained. A topological phase transition is induced by expanding or contracting the supercell, resulting in band inversion. Additionally, we propose topologically robust acoustic transmission along the one-dimensional edge. Furthermore, we discover that the proposed sonic crystal sustains zero-dimensional corner states, which can efficiently confine energy at subwavelength corners. These findings offer potential for the realization of subwavelength topological acoustic devices using realistic soft metamaterials.

Pseudo-spin switches and Aharonov-Bohm effect for topological boundary modes

Topological boundary modes in electronic and classical-wave systems exhibit fascinating properties. In photonics, topological nature of boundary modes can make them robust and endows them with an additional internal structure-pseudo-spins. Here, we introduce heterogeneous boundary modes, which are based on mixing two of the most widely used topological photonics platforms-the pseudo-spin-Hall-like and valley-Hall photonic topological insulators. We predict and confirm experimentally that transformation between the two, realized by altering the lattice geometry, enables a continuum of boundary states carrying both pseudo-spin and valley degrees of freedom (DoFs). When applied adiabatically, this leads to conversion between pseudo-spin and valley polarization. We show that such evolution gives rise to a geometrical phase associated with the synthetic gauge fields, which is confirmed via an Aharonov-Bohm type experiment on a silicon chip. Our results unveil a versatile approach to manipulating properties of topological photonic states and envision topological photonics as a powerful platform for devices based on synthetic DoFs.

Manipulation of Weyl Points in Reciprocal and Nonreciprocal Mechanical Lattices

We introduce feedback-measurement technologies to achieve flexible control of Weyl points and conduct the first experimental demonstration of Weyl type I-II transition in mechanical systems. We demonstrate that non-Hermiticity can expand the Fermi arc surface states from connecting Weyl points to Weyl rings, and lead to a localization transition of edge states influenced by the interplay between band topology and the non-Hermitian skin effect. Our findings offer valuable insights into the design and manipulation of Weyl points in mechanical systems, providing a promising avenue for manipulating topological modes in non-Hermitian systems.

Observation of Free-Boundary-Induced Chiral Anomaly Bulk States in Elastic Twisted Kagome Metamaterials

Chiral anomaly bulk states (CABSs) can be realized by choosing appropriate boundary conditions in a finite-size waveguide composed of two-dimensional Dirac semimetals, which have unidirectional and robust transport similar to that of valley edge states. CABSs use almost all available guiding space, which greatly improves the utilization of metamaterials. Here, free-boundary-induced CABSs in elastic twisted kagome metamaterials with C_{3v} symmetry are experimentally confirmed. The robust valley-locked transport and complete valley state conversion are experimentally observed. Importantly, the sign of the group velocity near the K and K^{'} points can be reversed by suspending masses at the boundary to manipulate the onsite potential. Moreover, CABSs are demonstrated in nanoelectromechanical phononic crystals by constructing an impedance-mismatched hard boundary. These results open new possibilities for designing more compact, space-efficient, and robust elastic wave macro- and microfunctional devices.

Focusing Micromechanical Polaritons in Topologically Nontrivial Hyperbolic Metasurfaces

Vertically stacked multiple atomically thin layers have recently widened the landscape of rich optical structures thanks to these quantum metamaterials or van der Waals (vdW) materials, featuring hyperbolic polaritons with unprecedented avenues for light. Despite their far-reaching implications, most of their properties rest entirely on a trivial band topological origin. Here, a 2D approach is adopted toward a micromechanical vdW analogue that, as a result of engineered chiral and mirror symmetries, provides topologically resilient hyperbolic radiation of mechanical vibrations in the ultrasonic regime. By applying laser vibrometry of the micrometer-sized metasurface, we are able to exhibit the exotic fingerprints of robust hyperbolic radiation spanning several frequencies, which beyond their physical relevance, may enable ultrasonic technologies.

Simultaneous pseudospin and valley topological edge states of elastic waves in phononic crystals made of distorted Kekulé lattices

Topological metamaterials protected by the spatial inversion symmetry mainly support single type edge state, interpreted by either the quantum valley Hall effect or the quantum spin Hall effect. However, owing to the existence of the complicated couplings and waveform conversions during elastic wave propagation, realizing topologically protected edge states that support both pseudospin and valley degrees of freedom in elastic system remains a great challenge. Here, we propose a two-dimensional Kekulé phononic crystal (PC) that can simultaneously possess pseudospin- and valley-Hall edge states in different frequency bands. By inhomogeneously changing the elliptical direction in a Kekulé lattice of elliptical cylinders, three complete phononic bandgaps exhibiting distinct topological phase transitions can be obtained, one of which supports a pair of pseudospin-Hall edge states and the other hosts valley-Hall edge states in the low and high frequency regime. Furthermore, a sandwiched PC heterostructure and a four-channel cross-waveguide splitter are constructed to achieve selective excitation and topological robust propagation of pseudospin- and valley-momentum locking edge states in a single configuration. These results provide new possibilities for manipulating in-plane bulk elastic waves with both pseudospin and valley degrees of freedom in a single configuration, which has potential applications for multiband and multifunctional waveguiding.

Topolectrical Circuit Correspondence Design of Polyacetylene

In cis and trans geometrical configurations of the polyacetylene molecule, one-dimensional chain is constructed by attaching a number of identical -HC=CH- units one-by-one. We attach as many units as required to obtain the chain of the desired length. In case of a very long polyacetylene chain, which is practically considered infinite in length, a periodic unit is defined, so that its band structure would be calculable. Then, the electronic properties and topological properties of the chain can be predicted. Since experimental synthesis of single-layer polyacetylene chain has lots of limitations, in an alternative approach, emulation of a tight-binding model is used to describe the electron transfer in polyacetylene polymer chain. In case of either synthesis or testing the polyacetylene molecule, it is necessary to improvise a one-to-one correspondence between polyacetylene polymer and topological circuit, which is introduced for the first time in the present study. To this aim, the outputs of density functional theory calculations alongside with the calculations based on the physical chemistry formalisms are used. Here, we observed that the electronic response of the circuit is topologically sustained at frequencies where the coupling was pre-determined via high precision quantum system equivalent topolectrical circuit, as an alternative classical system, to study electron transfer of trans-polyacetylene polymer quantum chain by the precision of one-electron.

Superwavelength self-healing of spoof surface sonic Airy-Talbot waves

Self-imaging phenomena for nonperiodic waves along a parabolic trajectory encompass both the Talbot effect and the accelerating Airy beams. Beyond the ability to guide waves along a bent trajectory, the self-imaging component offers invaluable advantages to lensless imaging comprising periodic repetition of planar field distributions. In order to circumvent thermoviscous and diffraction effects, we structure subwavelength resonators in an acoustically impenetrable surface supporting spoof surface acoustic waves (SSAWs) to provide highly confined Airy-Talbot effect, extending Talbot distances along the propagation path and compressing subwavelength lobes in the perpendicular direction. From a linear array of loudspeakers, we judiciously control the amplitude and phase of the SSAWs above the structured surface and quantitatively evaluate the self-healing performance of the Airy-Talbot effect by demonstrating how the distinctive scattering patterns remain largely unaffected against superwavelength obstacles. Furthermore, we introduce a new mechanism utilizing subwavelength Airy beam as a coding/decoding degree of freedom for acoustic communication with high information density comprising robust transport of encoded signals.

Photonic topological subspace-induced bound states in the continuum

Bound states in the continuum (BICs) are intriguing localized states that possess eigenvalues embedded within the continuum of extended states. Recently, a combination of topological band theory and BIC physics has given rise to a novel form of topological matter known as topological BICs. In this work, we experimentally demonstrate the photonic topological subspace-induced BICs. By using femtosecond-laser writing, we experimentally establish a photonic nontrivial three-leg ladder lattice, thereby directly observe the localized propagation of two kinds of topological edge states which exist at different boundaries. Interestingly, such edge states appear in the continuum of the bulk modes, and the topological properties are inherited from its independent subspace Hamiltonian which contains a celebrated Su-Schrieffer-Heeger lattice. This work not only presents a novel, to the best of our knowledge, platform for investigating topological physics in optics, but also unveils exciting prospects for future exploration of other remarkable BICs.

Anti-Parity-Time Symmetry in a Su-Schrieffer-Heeger Sonic Lattice

The Su-Schrieffer-Heeger (SSH) model is an important cornerstone in modern condensed-matter topology, yet it is the simplest one-dimensional (1D) tight binding approach to dwell into the characteristics of spinless electrons in chains of staggered bonds. Moreover, the chiral symmetry assures that its surface-confining states pin to zero energy, i.e., they reside midgap in the energy dispersion. Symmetry is also an attribute related to artificial media that are subject to parity P and time-reversal T operations. This non-Hermitian family has been thoroughly nourished in a wave-based context, where anti-PT (APT) symmetric systems are the youngest belonging members, permitting refractionless optics, inverse PT-symmetry breaking transition, and asymmetric mode switching. Here, we report the first extension of APT symmetry in an acoustic setting by endowing a SSH lattice with gain and loss components. We show that the in-gap topological defect state hinges on the non-Hermitian phase, in that the broken symmetry suppresses it, yet when PT or APT symmetry is intact, it is observed with either damped or evanescent decay, respectively. Our experiments showcase how the non-Hermitian SSH lattice serves as a utile platform to investigate topological properties across various PT symmetric phases using sound.