Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits

• Published in: Nature physics 2020-07, Vol.16 (7), p.747-750
• Main Authors: Helbig, T., Hofmann, T., Imhof, S., Abdelghany, M., Kiessling, T., Molenkamp, L. W., Lee, C. H., Szameit, A., Greiter, M., Thomale, R.
• Format: Article
• Language: English
• Subjects: 639/766/1130/2798; 639/766/119/2792; Atomic; Boundary conditions; Circuits; Classical and Continuum Physics; Complex Systems; Condensed Matter Physics; Eigenvalues; Eigenvectors; Electric potential; Electrical impedance; Energy conservation; Letter; Localization; Mathematical and Computational Physics; Metamaterials; Mode localization; Molecular; Open systems; Optical and Plasma Physics; Physics; Physics and Astronomy; Reciprocity; Skin effect; Theoretical; Topology; Voltage
• ISSN: 1745-2473; 1745-2481
• DOI: 10.1038/s41567-020-0922-9

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.