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Topolectrical-circuit realization of topological corner modes

Nature Physics volume 14, pages 925–929 (2018)Cite this article

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Abstract

Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological corner mid-gap states protected by the bulk spectral gap, reflection symmetries and a spectral symmetry. Here we introduce a topolectrical circuit design for realizing such corner modes experimentally and report measurements in which the modes appear as topological boundary resonances in the corner impedance profile of the circuit. Whereas the quantized bulk quadrupole moment of an electronic crystal does not have a direct analogue in the classical topolectrical-circuit framework, the corner modes inherit the identical form from the quantum case. Due to the flexibility and tunability of electrical circuits, they are an ideal platform for studying the reflection symmetry-protected character of corner modes in detail. Our work therefore establishes an instance where topolectrical circuitry is employed to bridge the gap between quantum theoretical modelling and the experimental realization of topological band structures.

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Fig. 1: Electrical circuit exhibiting a topological corner state with nodes of the circuit indicated by black dots.
Fig. 2: Comparison of experimental and theoretical results for the circuit spectrum and corner mode.

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Acknowledgements

We thank S. Huber and B. A. Bernevig for discussions. F.S. was supported by the Swiss National Science Foundation. We further acknowledge support by DFG-SFB 1170 TOCOTRONICS (project A07 and B04), by ERC-StG-Thomale- 336012-TOPOLECTRICS, by ERC-AG-3-TOP and by ERC-StG-Neupert-757867-PARATOP.

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Authors and Affiliations

  1. Experimentelle Physik 3, Physikalisches Institut, University of Würzburg, Würzburg, Germany

    Stefan Imhof, Christian Berger, Florian Bayer, Johannes Brehm, Laurens W. Molenkamp & Tobias Kiessling

  2. Department of Physics, University of Zurich, Zurich, Switzerland

    Frank Schindler & Titus Neupert

  3. Institute of High Performance Computing, Singapore, Singapore

    Ching Hua Lee

  4. Department of Physics, National University of Singapore, Singapore, Singapore

    Ching Hua Lee

  5. Institute for Theoretical Physics and Astrophysics, University of Würzburg, Würzburg, Germany

    Martin Greiter & Ronny Thomale

Authors
  1. Stefan Imhof
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  2. Christian Berger
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  3. Florian Bayer
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  4. Johannes Brehm
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  5. Laurens W. Molenkamp
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  7. Frank Schindler
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  8. Ching Hua Lee
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  9. Martin Greiter
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  10. Titus Neupert
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  11. Ronny Thomale
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Contributions

L.M., S.I., T.K., J.B., C.B. and F.B. were responsible for the circuit implementation and all measurements. F.S., S.I. and T.K. performed numerical simulations of the circuit. R.T., M.G., C.H.L., T.N. and F.S. conceived the project and developed the mapping from a Bloch Hamiltonian to topological circuitry.

Corresponding author

Correspondence to Ronny Thomale.

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Imhof, S., Berger, C., Bayer, F. et al. Topolectrical-circuit realization of topological corner modes. Nature Phys 14, 925–929 (2018). https://doi.org/10.1038/s41567-018-0246-1

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