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  • Letter
  • Open Access

Observation of cnoidal wave localization in nonlinear topolectric circuits

Hendrik Hohmann1, Tobias Hofmann1, Tobias Helbig1, Stefan Imhof2, Hauke Brand2, Lavi K. Upreti1,3, Alexander Stegmaier1, Alexander Fritzsche1, Tobias Müller1 et al.

Udo Schwingenschlögl4, Ching Hua Lee5, Martin Greiter1, Laurens W. Molenkamp2, Tobias Kießling2, and Ronny Thomale1,*

  • 1Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
  • 2Physikalisches Institut, Universität Würzburg, 97074 Würzburg, Germany
  • 3Universität Konstanz, Fachbereich Physik, 78457 Konstanz, Germany
  • 4Physical Sciences and Engineering Division (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
  • 5Department of Physics, National University of Singapore, 117542, Singapore

  • *Corresponding author: rthomale@physik.uni-wuerzburg.de
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Phys. Rev. Research 5, L012041 – Published 21 March, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L012041

Abstract

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.

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Phys. Rev. Research 5, L012041– Published 21 March, 2023
  • Received 29 July 2022
  • Accepted 22 November 2022
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