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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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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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.
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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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DOI: https://doi.org/10.1038/s41567-018-0246-1
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