Non-Hermitian topological whispering gallery.

In 1878, Lord Rayleigh observed the highly celebrated phenomenon of sound waves that creep around the curved gallery of St Paul's Cathedral in London1,2. These whispering-gallery waves scatter efficiently with little diffraction around an enclosure and have since found applications in ultrasonic fatigue and crack testing, and in the optical sensing of nanoparticles or molecules using silica microscale toroids. Recently, intense research efforts have focused on exploring non-Hermitian systems with cleverly matched gain and loss, facilitating unidirectional invisibility and exotic characteristics of exceptional points3,4. Likewise, the surge in physics using topological insulators comprising non-trivial symmetry-protected phases has laid the groundwork in reshaping highly unconventional avenues for robust and reflection-free guiding and steering of both sound and light5,6. Here we construct a topological gallery insulator using sonic crystals made of thermoplastic rods that are decorated with carbon nanotube films, which act as a sonic gain medium by virtue of electro-thermoacoustic coupling. By engineering specific non-Hermiticity textures to the activated rods, we are able to break the chiral symmetry of the whispering-gallery modes, which enables the out-coupling of topological 'audio lasing' modes with the desired handedness. We foresee that these findings will stimulate progress in non-destructive testing and acoustic sensing.

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.

Structured sonic tube with carbon nanotube-like topological edge states.

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.