Observation of cnoidal wave localization in non-linear topolectric circuits

TL;DR

This paper reports the experimental observation of a localized cnoidal wave state in a non-linear topoelectric circuit, demonstrating how non-linearity and topology interplay to produce novel localized wave phenomena.

Contribution

It introduces the observation of a localized cnoidal wave state in a non-linear SSH circuit, linking non-linearity, topology, and wave localization in electric circuits.

Findings

The voltage response follows the Korteweg-de Vries equation.

The topological boundary state distorts into a cnoidal wave in the non-linear regime.

Cnoidal eccentricity varies from edge to bulk.

Abstract

We observe a localized cnoidal (LCn) state in an electric circuit network. Its formation derives from the interplay of non-linearity and the topology inherent to a Su-Schrieffer-Heeger (SSH) chain of inductors. Varicap diodes act as voltage-dependent capacitors, and create a non-linear on-site potential. For a sinusoidal voltage excitation around midgap frequency, we show that the voltage response in the non-linear SSH circuit follows the Korteweg-de Vries equation. The topological SSH boundary state which relates to a midgap impedance peak in the linearized limit is distorted into the LCn state in the non-linear regime, where the cnoidal eccentricity decreases from edge to bulk.