Observation of cnoidal wave localization in nonlinear topolectric circuits

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.

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

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.

American Physical Society (APS)

Physical Review Research



Additional Links

Permanent link to this record

Version History

Now showing 1 - 2 of 2
2023-03-23 06:13:31
Published in journal
2022-06-26 10:45:02
* Selected version