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.

拓扑边缘模式是位于材料边缘的激发，但其特征是在本体中定义了拓扑不变量。这种体-边对应关系使得能够在从冷原子到超材料，活性物质和地球物理流的各种系统中创建强大的电子，电磁和机械传输特性。最近，非赫米特拓扑系统（其中能量不守恒）的出现激发了相当大的理论进展。特别地，已经引入了只能在非埃尔米特系统中存在的新颖拓扑阶段。但是，是否可以通过实验观察到这些相及其性质，仍然是一个悬而未决的问题。这里，我们确定并观察到了特定非Hermitian拓扑阶段的体-边对应形式。我们发现，大量非Hermitian拓扑不变量的变化会导致拓扑边缘模式局部化以及独特的纯粹非Hermitian特性的变化。使用从量子到经典的类比，我们创建了具有不可逆相互作用的机械超材料，在该材料中，我们通过实验观察了预测的体-边对应关系，从而证明了其鲁棒性。我们的结果为非Hermitian拓扑领域和以前所未有的方式操纵波开辟了道路。我们创建了一个具有不可逆相互作用的机械超材料，在该材料中，我们通过实验观察了预测的体积-边沿对应​​关系，从而证明了其坚固性。我们的结果为非Hermitian拓扑领域和以前所未有的方式操纵波开辟了道路。我们创建了一个具有不可逆相互作用的机械超材料，在该材料中，我们通过实验观察了预测的体积-边沿对应​​关系，从而证明了其坚固性。我们的结果为非Hermitian拓扑领域和以前所未有的方式操纵波开辟了道路。