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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 ofsystems, from cold atoms to metamaterials, active matter and geophysical flows.Recently, the advent of non-Hermitian topological systems---wherein energy isnot conserved---has sparked considerable theoretical advances. In particular,novel topological phases that can only exist in non-Hermitian systems have beenintroduced. However, whether such phases can be experimentally observed, andwhat their properties are, have remained open questions. Here, we identify andobserve a novel form of bulk-edge correspondence for a particular non-Hermitiantopological phase. We find that a change in the bulk non-Hermitian topologicalinvariant leads to a change of topological edge mode localisation together withpeculiar purely non-Hermitian properties. Using a quantum-to-classical analogy,we create a mechanical metamaterial with non-reciprocal interactions, in whichwe observe experimentally the predicted bulk-edge correspondence, demonstratingits robustness. Our results open new avenues for the field of non-Hermitiantopology and for manipulating waves in unprecedented fashions.

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