Higher-order exceptional ring semimetal with real hinge states in acoustic metamaterials.

Non-Hermitian topological phase, with the novel concepts such as exceptional points and the skin effect, has opened up a new paradigm beyond Hermitian topological physics. Exceptional ring semimetal, featured by a stable ring of exceptional points in three dimensions, exhibits first-order topological properties, including topological surface states and a surface-dependent skin effect. Nevertheless, despite extensive research on Hermitian higher-order insulators and semimetals, higher-order exceptional ring semimetal is just emerging. Here, we report the first realization of a higher-order Weyl exceptional ring semimetal in a three-dimensional lossy acoustic metamaterial. The non-Hermitian higher-order topology is reflected in the topological hinge states and a hinge-dependent skin effect. Counterintuitively, the topological hinge states maintain purely real energy even under a high loss level, ensuring robust hinge-state propagation. Our findings evidence the non-Hermitian higher-order bulk-boundary correspondence of exceptional ring semimetal, and may pave the way for non-Hermitian functional acoustic devices.