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arXiv · 2206.09931

Observation of cnoidal wave localization in non-linear topolectric circuits

Hendrik Hohmann·Tobias Hofmann·Tobias Helbig·Stefan Imhof·Hauke Brand·Lavi K. Upreti·Alexander Stegmaier·Alexander Fritzsche·Tobias Müller·Udo Schwingenschlögl·Ching Hua Lee·Martin Greiter·Laurens W. Molenkamp·Tobias Kießling·Ronny Thomale
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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.

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Hendrik Hohmann, Tobias Hofmann, Tobias Helbig, Stefan Imhof, Hauke Brand, Lavi K. Upreti, Alexander Stegmaier, Alexander Fritzsche, Tobias Müller, Udo Schwingenschlögl, Ching Hua Lee, Martin Greiter, Laurens W. Molenkamp, Tobias Kießling, Ronny Thomale. 2022-06-20. Observation of cnoidal wave localization in non-linear topolectric circuits. https://doi.org/10.1103/physrevresearch.5.l012041

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