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Topological edge states in the frequency dimension and their realization with Floquet electrical circuits

Alexander Stegmaier1,*, Alexander Fritzsche1, Riccardo Sorbello1, Martin Greiter1, Hauke Brand2, Christine Barko2, Maximilian Hofer2, Udo Schwingenschlögl3, Roderich Moessner4,5 et al.

Ching Hua Lee6,†, Alexander Szameit5,7, Andrea Alù8,9, Tobias Kießling2,5, and Ronny Thomale1,5,‡

  • *Contact author: alexander.stegmaier@uni-wuerzburg.de
  • †Contact author: phylch@nus.edu.sg
  • ‡Contact author: ronny.thomale@uni-wuerzburg.de
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Phys. Rev. Research 7, 043118 – Published 31 October, 2025

DOI: https://doi.org/10.1103/6n5m-wvs7

Abstract

We build Floquet-driven capacitive circuit networks to realize topological states of matter in the frequency domain. As visible through our Floquet Laplacian formalism, the intertwining of static circuit components and parametric Floquet driving effectively creates a barrier in the frequency dimension, allowing to resolve the bulk-boundary correspondence of Floquet topological matter. By implementing a Su-Schrieffer-Heeger Floquet lattice model and measuring the associated circuit Laplacian and characteristic resonances, we demonstrate Floquet topological edge modes emerging at this frequency space barrier. Floquet circuits allow for the creation of topological phenomena in synthetic frequency dimensions with just a single unit cell of time-variable circuit components.

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Outline

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Phys. Rev. Research 7, 043118– Published 31 October, 2025
  • Received 17 July 2024
  • Revised 21 January 2025
  • Accepted 23 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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