Open and closed boundary correspondence in non-reciprocal metamaterials

Recently, the advent of non-Hermitian topological systems—wherein energy is not conserved—has sparked considerable theoretical advances. In particular, skin effect and novel topological phases that can only exist in non-Hermitian systems have been introduced. In all these phenomena the critical relation in open and closed boundary condition for non-Hermitian one-dimensional chain is still under speculation with immense curiosity. We will discuss the theoretical inventories of such correspondences and demonstrate their experimental realizations in non-Hermitian metamaterials. With quantum-to-classical analogy we create mechanical metamaterials with non-reciprocal interactions to mimic non-Hermiticity, in which our predicted open-closed or bulk-boundary correspondence has been observed experimentally. It shows for a topological chain, a change in the bulk corresponds to a change of localization of the topological edge mode. Such unfamiliar bulk boundary correspondence has also been manifested in the metamaterial to manipulate waves in unprecedented fashions. These techniques are useful to engineer wave properties, steering waves on demand, in sensing and energy harvesting.