Observation of non-Hermiticity-induced topological edge states in the continuum in a trimerized elastic lattice

Topologically protected localized states are commonly existent inside bulk band gaps with topological features, which, however, can be shifted to coexist with a continuous spectrum under particular coupling modulations, forming the so-called topological bound states in the continuum (BICs). These embedded topological states have so far been derived under the Hermitian assumptions that neglect the influence of nonconservative characteristics of classical wave systems on the topological properties. In this study, with a one-dimensional trimerized elastic lattice, we report the experimental demonstration of topological edge states in the continuum produced solely by non-Hermiticity, without additional coupling modulation. The trimerized elastic lattice is a chain of plates connected through thin beams, with the non-Hermiticity introduced by attaching constrained damping layers to particular sites in the chain assembly. We prove that appropriately tailored non-Hermitian modulation can induce topological edge states that appear in the bulk spectrum rather than exist in the band gap. Besides, the existence of such topological edge states is observed to be closely linked to the configurations of the lattice boundaries. This study affirms that non-Hermiticity can play an important role in creating topological BICs, gaining insight into the non-Hermitian topological physics and offering interesting avenues for exploring sophisticated non-Hermitian topological phenomena including higher-order topology in the continuum.