Observation of cnoidal wave localization in nonlinear topolectric circuits

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.

Citation
Hohmann, H., Hofmann, T., Helbig, T., Imhof, S., Brand, H., Upreti, L. K., Stegmaier, A., Fritzsche, A., Müller, T., Schwingenschlögl, U., Lee, C. H., Greiter, M., Molenkamp, L. W., Kießling, T., & Thomale, R. (2023). Observation of cnoidal wave localization in nonlinear topolectric circuits. Physical Review Research, 5(1). https://doi.org/10.1103/physrevresearch.5.l012041

Acknowledgements
We thank Aurelien Manchon for useful discussions. The work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 258499086 - SFB 1170 and through the WürzburgDresden Cluster of Excellence on Complexity and Topology in Quantum Matter–ct.qmat Project-ID 390858490 - EXC 2147. C.H.L. is funded by Singapore’s Ministry of Education Tier-I grant (WBS A-8000022-00-00). We acknowledge funding from King Abdullah University of Science and Technology (KAUST) under Award 2022-CRG10-4660. T.He. was supported by a Ph.D. scholarship of the Studienstiftung des Deutschen Volkes.

Publisher
American Physical Society (APS)

Journal
Physical Review Research

DOI
10.1103/physrevresearch.5.l012041

arXiv
2206.09931

Additional Links
https://link.aps.org/doi/10.1103/PhysRevResearch.5.L012041

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