Observation of non-Hermitian topology and its bulk–edge correspondence in an active mechanical metamaterial

Significance In recent years, the mathematical concept of topology has been used to predict and harness the propagation of waves such as light or sound in materials. However, these advances have so far been realized in idealized scenarios, where waves do not attenuate. In this research, we demonstrate that topological properties of a mechanical system can predict the localization of waves in realistic settings where the energy can grow and/or decay. These findings may lead to strategies to manipulate waves in unprecedented fashions, for applications in vibration damping, energy harvesting, and sensing technologies. Topological edge modes are excitations that are localized at the materials’ edges and yet are characterized by a topological invariant defined in the bulk. Such bulk–edge correspondence has enabled the creation of robust electronic, electromagnetic, and mechanical transport properties across a wide range of systems, from cold atoms to metamaterials, active matter, and geophysical flows. Recently, the advent of non-Hermitian topological systems—wherein energy is not conserved—has sparked considerable theoretical advances. In particular, novel topological phases that can only exist in non-Hermitian systems have been introduced. However, whether such phases can be experimentally observed, and what their properties are, have remained open questions. Here, we identify and observe a form of bulk–edge correspondence for a particular non-Hermitian topological phase. We find that a change in the bulk non-Hermitian topological invariant leads to a change of topological edge-mode localization together with peculiar purely non-Hermitian properties. Using a quantum-to-classical analogy, we create a mechanical metamaterial with nonreciprocal interactions, in which we observe experimentally the predicted bulk–edge correspondence, demonstrating its robustness. Our results open avenues for the field of non-Hermitian topology and for manipulating waves in unprecedented fashions.