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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. This work was supported by the National Basic Research Program of China (2017YFA0303702), NSFC (12074183, 11922407, 11904035, 11834008, 11874215 and 12104226) and the Fundamental Research Funds for the Central Universities (020414380181). Z.Z. acknowledges the support from the China National Postdoctoral Program for Innovative Talents (BX20200165) and the China Postdoctoral Science Foundation (2020M681541). L.Z. acknowledges support from the CONEX-Plus programme funded by Universidad Carlos III de Madrid and the European Union's Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreement 801538. J.C. acknowledges support from the European Research Council (ERC) through the Starting Grant 714577 PHONOMETA and from the MINECO through a Ramón y Cajal grant (grant number RYC-2015-17156).

The existence of topologically protected boundary states in the Su–Schrieffer–Heeger (SSH) model has been widely explored in various systems in the past decades. On the other hand, a seemingly irrelevant phenomenon of Tamm mode, a defect mode caused by elaborately introducing perturbation into the trivial structures, has also attracted enormous interest. In this Letter, we bridge the gap between acoustic Tamm mode and its correlation rule with typical topological acoustic mode. Starting from the 1D acoustic cavity-based SSH model, the topologically protected edge modes in a complete bandgap are achieved. Through modulating the height of boundary cavity, we find two types of Tamm edge modes both numerically and experimentally and grasp their distinct variation tendency from the topologically protected edge modes. Furthermore, we extend the study to 2D higher-order topological acoustic systems and the lower-dimensional Tamm corner modes are clearly observed. We foresee that the multi-frequency sound confinement introduced by the Tamm localized modes may open a revealing landscape for acoustic functional devices.

Traditional topological insulators support the topologically protected boundary states that are one dimension lower than the system itself. Recently, higher-order topological insulators have received increasing attention in the field of acoustic wave manipulation due to their unique bulk-boundary correspondence principle, hosting both gapped edge states and in-gap corner states simultaneously. However, for most of the topological acoustic systems, the lack of reconfigurability and the inevitable outer trivial regions with considerable thickness restrict the potential applications of acoustic topological insulators. Here, we experimentally demonstrate a reconfigurable condensed acoustic second-order topological insulator in free space by using subwavelength soda cans whose side length is significantly reduced to 1.89 times of the corresponding wavelength. The topological nontrivial phase is introduced through tunably modulating the interval between cans. Without the typically required outer trivial regions, we observe the topological corner states at the corner of the finite structures in both simulations and experiments. Furthermore, the robustness against the defects induced by dislocations and deformations is discussed. We foresee that the proposal may facilitate the application potentials of topological acoustics in low-frequency sound manipulations.