Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits - Helbig, T.; Hofmann, T.; Imhof, S.; Abdelghany, M.; Kiessling, T.; Molenkamp, L. W.; Lee, C. H.; Szameit, A.; Greiter, M.; Thomale, R. (Nature physics, 2020)
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 matter 1 , 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 bulk 3 , 4 . The presence of gain and loss, in combination with the violation of reciprocity, has been predicted to affect this principle dramatically 5 , 6 . Here, we report the experimental observation of BBC violation in a non-reciprocal topolectric circuit 7 , 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.