Acoustic non-Hermitian Dirac states tuned by flexible designed gain and loss

Non-Hermitian Dirac point plays an important role in topological transition as their Hermitian counterpart and connect non-Hermitian physics with band topology. Instead of being exceptional point or exceptional ring, we here reveal that the Dirac points can be survived in the presence of gain and loss obeying anti-parity-time symmetry based on the two-dimensional inclined Su–Schrieffer–Heeger model. Particularly, such non-Hermitian parameters enable the engineering of non-Hermitian Dirac states, including shift of the Dirac points and topological transition from Dirac semimetal to weak topological insulator. We experimentally demonstrate these non-Hermitian Dirac states in acoustic crystal, where the gain and loss are, respectively, controlled by the active acoustic components and absorbing materials. Through varying the strength of gain and loss, the shifting and opening of the Dirac points, together with topological edge states, are observed. Our system serves as an ideal and highly tunable platform for exploring the non-Hermitian topological physics and has potential applications in designing acoustic devices.