# Observation of bulk boundary correspondence breakdown in topolectrical circuits

## TL;DR

This paper experimentally demonstrates the breakdown of bulk-boundary correspondence in a non-reciprocal topolectric circuit, revealing boundary-sensitive admittance modes and non-local voltage responses that challenge traditional topological classifications.

## Contribution

It provides the first experimental observation of BBC violation in topolectric circuits with gain, loss, and non-reciprocity, highlighting new boundary phenomena in non-Hermitian topological systems.

## Key findings

- Admittance spectrum shows boundary-sensitive localization.
- Non-local voltage response depends on boundary position.
- BBC violation observed in non-reciprocal topolectric circuit.

## Abstract

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 like gain and loss, or periodic driving, qualitatively amends these laws. A contemporary frontier of meta-material research is the challenge open systems pose to the established characterization of topological matter. There, one of the most relied upon principles is the bulk-boundary correspondence (BBC), which intimately relates the properties of the surface states to the topological classification of the bulk. The presence of gain and loss, in combination with the violation of reciprocity, has recently been predicted to affect this principle dramatically. Here, we report the experimental observation of BBC violation in a non-reciprocal topolectric circuit. 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 AC 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.