# Active topolectrical circuits

## TL;DR

This paper introduces active topolectrical circuits that combine topological protection with autonomous self-organization, enabling robust edge oscillations through nonlinear components, with theoretical, simulation, and experimental validation.

## Contribution

It unifies topological concepts with active matter principles to design self-exciting circuits exhibiting protected edge states, a novel integration of these fields.

## Key findings

- Demonstrated self-organized protected edge oscillations in 1D and 2D circuits.
- Validated theoretical predictions with experiments and simulations.
- Showed robustness and versatility of nonlinear active topolectrical circuits.

## Abstract

The transfer of topological concepts from the quantum world to classical mechanical and electronic systems has opened fundamentally new approaches to protected information transmission and wave guidance. A particularly promising technology are recently discovered topolectrical circuits that achieve robust electric signal transduction by mimicking edge currents in quantum Hall systems. In parallel, modern active matter research has shown how autonomous units driven by internal energy reservoirs can spontaneously self-organize into collective coherent dynamics. Here, we unify key ideas from these two previously disparate fields to develop design principles for active topolectrical circuits (ATCs) that can self-excite topologically protected global signal patterns. Realizing autonomous active units through nonlinear Chua diode circuits, we theoretically predict and experimentally confirm the emergence of self-organized protected edge oscillations in one- and two-dimensional ATCs. The close agreement between theory, simulations and experiments implies that nonlinear ATCs provide a robust and versatile platform for developing high-dimensional autonomous electrical circuits with topologically protected functionalities.