Interlayer coupling induced extended state in a localized continuum of non-Hermitian topolectrical circuits

Bound states in the continuum (BICs) are spatially localized states whose eigenvalues are situated within the continuum of extended states. Recent research has demonstrated that the interaction between BICs and the non-Hermitian skin effect (NHSE) can give rise to an extended state in a localized continuum (ELC), which is essentially the inverse of the BICs. Here, we propose and experimentally demonstrate a very general and simple approach for the generation of the ELC in a mirror-stacking system. This approach allows the Hamiltonian of the bilayer system to be decoupled into two topological subspaces. Upon tuning the interlayer coupling, the BICs are realized when the topological bound states spectrally overlap with the bulk band. The ELC arises with the introduction of the NHSE, which not only transforms all bulk modes into skin modes but also concurrently delocalizes the bound state. As a representative example, we experimentally realize the ELC in a mirror-stacked non-Hermitian Su-Schrieffer-Heeger electric circuit. Our findings are expected to expand the research significance of NHSE and ELCs.