Exceptional points of acoustic topological boundary states

Spectral and band topologies have different degrees of freedom, usually treated separately. Recent studies have shown that spectral topology is not only related to the topological phase transition of bulk bands but can also influence the original boundary states. However, the interplay of these two topologies remains elusive, and the rich phase transitions resulting from their combination have yet to be explored. Here, we construct a two-dimensional non-Hermitian topological acoustic model using honeycomb-lattice cavity-tube configurations with controllable in-plane hopping and out-of-plane radiation losses. The phase diagram obtained is based on the interaction between trivial and nontrivial topological bands and unbroken and broken parity-time symmetry, depending on the hopping difference and loss strength trade-off. We experimentally observe novel exceptional points of topological boundary states, indicating that the energy band attraction effect is more substantial for the boundary than for the bulk. These results enrich non-Hermitian topological physics and may lead to robust yet ultrasensitive sensing applications by taking advantage of both topological and parity-time systems.