Solitons and topology: Observation of cnoidal wave localization in non-linear topolectric circuits

ORAL

Abstract

Topological phases have been realized in a variety of classical metamaterials. They provide easily accessible platforms to study topology in regimes beyond experimental limitations of real materials. While most implementations are limited to the linear regime, investigating non-linear effects promises to reveal a plethora of new phenomena, such as solitons and chaos. To study the intertwining of topology and non-linearity we engineered a topolectric circuit reminiscent of the Su-Schrieffer-Heeger (SSH) model with added tunable onsite non-linearity. We observe the localized cnoidal (LCn) state which maintains the spatial exponential localization of the SSH edge mode while distorting a sinusoidal input into eccentric waves in time domain. In this talk, we complement the non-linear differential equations with the theory of topological localization and develop an analytic description of the LCn state.

*The work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 258499086 - SFB 1170 and through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter – ct.qmat Project-ID 390858490 - EXC 2147.

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Publication: H. Hohmann et al. Observation of cnoidal wave localization in non-linear topolectric circuits, arXiv:2206.09931; submitted to PRR

Presenters

  • Hendrik Hohmann

    • Julius-Maximilians University of Wuerzburg

Authors

  • Hendrik Hohmann

    • Julius-Maximilians University of Wuerzburg

  • Tobias Hofmann

    • Julius-Maximilians University of Wuerzburg

  • Tobias Helbig

    • Julius-Maximilians University of Wuerzburg

  • Lavi K Upreti

    • Julius-Maximilians-Universität of Würzburg

  • Alexander Stegmaier

    • Julius-Maximilians-University Wuerzburg

  • Alexander Fritzsche

    • Julius-Maximilians-University of Wuerzburg

  • Tobias Müller

    • Julius-Maximilians-Universität Würzburg
    • Julius-Maximilians University of Wuerzburg
    • Julius-Maximilians-Universitaet Wuerzburg
    • Julius-Maximilians-University of Wuerzburg

  • Ching Hua Lee

    • Natl Univ of Singapore

  • Martin Greiter

    • Julius-Maximilians University of Wuerzburg

  • Ronny Thomale

    • Julius-Maximilians University of Wuerzburg
    • Julius-Maximilians University of Wuerzbu
    • Institut für Theoretische Physik und Astrophysik Universität Würzburg, 97074 Würzburg, Germany
    • University of Wuerzburg