Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits

The study of the laws of nature has traditionally been pursued in the limit of isolated systems, where energy is conserved. This is not always a valid approximation, however, as the inclusion of features such as gain and loss, or periodic driving, qualitatively amends these laws. A contemporary frontier of metamaterial research is the challenge open systems pose to the characterization of topological matter1,2. Here, one of the most relied upon principles is the bulk–boundary correspondence (BBC), which intimately relates the surface states to the topological classification of the bulk3,4. The presence of gain and loss, in combination with the violation of reciprocity, has been predicted to affect this principle dramatically5,6. Here, we report the experimental observation of BBC violation in a non-reciprocal topolectric circuit7, which is also referred to as the non-Hermitian skin effect. The circuit admittance spectrum exhibits an unprecedented sensitivity to the presence of a boundary, displaying an extensive admittance mode localization despite a translationally invariant bulk. Intriguingly, we measure a non-local voltage response due to broken BBC. Depending on the a.c. current feed frequency, the voltage signal accumulates at the left or right boundary, and increases as a function of nodal distance to the current feed. Boundary-localized bulk eigenstates given by the non-Hermitian skin effect are observed in a non-reciprocal topological circuit. A fundamental revision of the bulk–boundary correspondence in an open system is required to understand the underlying physics.