Engineering Higher-Order Topological Confinement via Acoustic Non-Hermitian Textures

Higher-order topological insulators are a newly unveiled category of topological materials, distinguished by their exceptional characteristics absent in conventional topological insulators, e.g., 1D hinge states, or zero-dimensional corner states, for instance. Adding attenuating or amplifying components manifest even richer and more intricate non-Hermitian topological properties. While losses, for the most part, come for free, decorating topological systems with the gain counterpart poses significant challenges. Here, a non-Hermitian second-order topological insulator (SOTI) is constructed for a sonic demonstration, by bestowing a cavity-based lattice both with electro-thermoacoustic gain and loss. The inner cavity walls are decorated with electrically biased carbon nanotube films to be able to manipulate spatially and in strength, a non-Hermitian response at will. These measurements demonstrate that this flexibility allows us to design highly unconventional interface and corner confining topologies by decisively engineering gain and loss textures within the unit cell. It is foreseen that the advances may enable new avenues for energy harvesting and fundamental understanding in condensed matter and classical topological physics.