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

doi:10.1103/physrevresearch.5.l012041

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 journal › Article › peer-review

18 Scopus citations

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.

Original language	English (US)
Journal	Physical Review Research
Volume	5
Issue number	1
DOIs	https://doi.org/10.1103/physrevresearch.5.l012041
State	Published - Mar 21 2023

Bibliographical note

KAUST 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.

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10.1103/physrevresearch.5.l012041

https://repository.kaust.edu.sa/bitstream/10754/679348/5/PhysRevResearch.5.L012041.pdf

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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

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title = "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.",

author = "Hendrik Hohmann and Tobias Hofmann and Tobias Helbig and Stefan Imhof and Hauke Brand and Upreti, {Lavi K.} and Alexander Stegmaier and Alexander Fritzsche and Tobias M{\"u}ller and Udo Schwingenschl{\"o}gl and Lee, {Ching Hua} and Martin Greiter and Molenkamp, {Laurens W.} and Tobias Kie{\ss}ling and Ronny Thomale",

note = "KAUST 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 W{\"u}rzburgDresden Cluster of Excellence on Complexity and Topology in Quantum Matter–ct.qmat Project-ID 390858490 - EXC 2147. C.H.L. is funded by Singapore{\textquoteright}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.",

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AU - Hohmann, Hendrik

AU - Hofmann, Tobias

AU - Helbig, Tobias

AU - Imhof, Stefan

AU - Brand, Hauke

AU - Upreti, Lavi K.

AU - Stegmaier, Alexander

AU - Fritzsche, Alexander

AU - Müller, Tobias

AU - Schwingenschlögl, Udo

AU - Lee, Ching Hua

AU - Greiter, Martin

AU - Molenkamp, Laurens W.

AU - Kießling, Tobias

AU - Thomale, Ronny

N1 - KAUST 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.

PY - 2023/3/21

Y1 - 2023/3/21

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/679348

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M3 - Article

SN - 2643-1564

VL - 5

JO - Physical Review Research

JF - Physical Review Research

IS - 1

ER -

Observation of cnoidal wave localization in nonlinear topolectric circuits

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