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 language||English (US)|
|Journal||Physical Review Research|
|State||Published - Mar 21 2023|
Bibliographical noteKAUST Repository Item: Exported on 2023-03-24
Acknowledged KAUST grant number(s): 2022-CRG10-4660
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.