# Reciprocal skin effect and its realization in a topolectrical circuit

## TL;DR

This paper introduces the reciprocal skin effect in non-Hermitian, reciprocal systems across multiple dimensions, demonstrating it experimentally in a circuit and discussing potential applications in wave detection.

## Contribution

It presents the first experimental realization of the reciprocal skin effect in a topolectrical circuit, expanding the understanding of non-Hermitian topological phenomena.

## Key findings

- Reciprocal skin effect causes opposite localization for modes with opposite momentum.
- Experimental demonstration in a passive RLC circuit confirms theoretical predictions.
- Potential applications include directional and polarization electromagnetic wave detectors.

## Abstract

A system is non-Hermitian when it exchanges energy with its environment and non-reciprocal when it behaves differently upon the interchange of input and response. Within the field of metamaterial research on synthetic topological matter, the skin effect describes the conspiracy of non-Hermiticity and non-reciprocity to yield extensive anomalous localization of all eigenmodes in a (quasi) one-dimensional geometry. Here, we introduce the reciprocal skin effect, which occurs in non-Hermitian but reciprocal systems in two or more dimensions: Eigenmodes with opposite longitudinal momentum exhibit opposite transverse anomalous localization. We experimentally demonstrate the reciprocal skin effect in a passive RLC circuit, suggesting convenient alternative implementations in optical, acoustic, mechanical, and related platforms. Skin mode localization brings forth potential applications in directional and polarization detectors for electromagnetic waves.