Observation of cnoidal wave localization in nonlinear 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

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We observe a localized cnoidal (LCn) state in an electric circuit network. Its formation derives from the interplay of nonlinearity and the topology inherent to a Su-Schrieffer-Heeger (SSH) chain of inductors. Varicap diodes act as voltage-dependent capacitors, and create a nonlinear on-site potential. For a sinusoidal voltage excitation around midgap frequency, we show that the voltage response in the nonlinear 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 nonlinear regime, where the cnoidal eccentricity decreases from edge to bulk.
Original languageEnglish (US)
JournalPhysical Review Research
Issue number1
StatePublished - Mar 21 2023


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