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 $\mathcal{P}$ and time-reversal $\mathcal{T}$ operations. This non-Hermitian family has been thoroughly nourished in a wave-based context, where anti-$\mathcal{P}\mathcal{T}$ ($\mathcal{A}\mathcal{P}\mathcal{T}$) symmetric systems are the youngest belonging members, permitting refractionless optics, inverse $\mathcal{P}\mathcal{T}$-symmetry breaking transition, and asymmetric mode switching. Here, we report the first extension of $\mathcal{A}\mathcal{P}\mathcal{T}$ 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 $\mathcal{P}\mathcal{T}$ or $\mathcal{A}\mathcal{P}\mathcal{T}$ 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 $\mathcal{P}\mathcal{T}$ symmetric phases using sound.

Over the recent decade, topological insulators, originating from the condensed matter physics, have resided at the frontier in the field of acoustics owing to their novel topological properties for manipulating robust wave propagation, which have also opened an intriguing landscape for potential applications. At the meantime, gradually slowing down acoustic waves with metamaterials allows temporary storage of sound, leading to the exploration of so-called trapped rainbow. However, most of the current studies are reported in a topological trivial context with complex structures, and it is hitherto still a challenge to obtain the high-efficient acoustic rainbow trapping effect in a straightforward setup. Here, we propose an acoustic gradient topological insulator in the one-dimensional system to realize a highly efficient rainbow trapping device. Based on the acoustic analogous Su–Schrieffer–Heeger model, we tune the eigenfrequencies of the topological interface states through modulating the neck widths of Helmholtz resonators. The experimentally measured pressure spectra clearly show that the proposed structure could tightly trap the broad-band sound waves at the target spatial positions. Our proposal may provide versatile possibilities for the design of topological acoustic devices.

A single-wall carbon nanotube can be viewed as a one-dimensional material created by rolling up a sheet of graphene. Its electronic band structure depends on the chirality, i.e., how the sheet has been rolled up, yet synthesizing the symmetry at will is rather challenging. We structure an artificial honeycomb lattice in both a zigzag and an armchair tube and explore their topological features for sound. Our findings reveal how armchair tubes remain gapless, whereas the zigzag counterparts host nontrivial edge states of non-zero quantized Zak phase, which are dictated by the circumferential number of units. Unlike man-made planar lattices whose underling symmetry must be broken to harvest quantum Hall and pseudospin phases, interestingly, the structured tubular lattice symmetry remains intact, while its nontrivial phase alone is governed by the chirality and the tube diameter. We foresee that our results, not only for sound, but also in photonics, mechanics and electronics will broaden future avenues for fundamental and applied sciences.

Higher-order topological insulator hosts both gapped edge states and in-gap corner states, which has garnered considerable attentions in the field of condensed matter physics, and most recently is further extended to the classical wave systems. Conventional acoustic metamaterials have intrinsic material and design limitations that prevent them from being used to create such states in subwavelength scale with function reconfigurability. Recently, the acoustic second-order topological insulators (SOTIs) composed of locally resonant metamaterials were reported to solve the problem, where the topological phase transition is induced by shrinking/expanding metamolecules. Here, we propose an acoustic SOTI in subwavelength scale by another protocol, i.e. gliding metamolecules, and the SOTI is pinned in the nontrivial region without the regular topological phase transition. Soda cans metamaterials in free space are utilized to support the spoof surface acoustic waves. With varying the introduced glided angle, the switching from the bulk to edge and corner states can be achieved accordingly. Furthermore, we not only experimentally observe this state switching process, but also illustrate the robustness of the topological corner states against various defects. Our results provide versatile ways to launch acoustic lower-dimensional topological states that might lead to interesting sound concentration applications.