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Braiding reflectionless states in non-Hermitian magnonics

Nature Physics volume 20, pages 1904–1911 (2024)Cite this article

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Abstract

A thorough understanding of the topological classifications of non-Hermitian energy bands is essential for advancing non-Hermitian band theory and its applications. As evidenced in various disciplines of physics, including optics, electronics and acoustics, the process of braiding plays a crucial role in the classification of non-Hermitian bands that manifest topological characteristics. Here we demonstrate topological braiding of both reflectionless states and resonant states in non-Hermitian magnons, unveiling a reversal in their braiding handedness. Furthermore, we constitute parity–time symmetric reflectionless scattering modes, along with their degenerate exceptional points. Our results not only underscore the importance of braided scattering states, but also establish magnonics as a versatile platform for exploring non-Hermitian band theory and developing magnon-based applications, including topological energy transfer, tunable absorbers and logic circuits.

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Fig. 1: The experimental demonstration of HRZ by realizing the PT of RSMs.
Fig. 2: EPs detected experimentally in the 3D synthetic parameter space.
Fig. 3: Opposite handedness braids of the complex eigenvalues of HRZ and Hres.
Fig. 4: Arbitrary numbers of braids are determined by the choice of paths punctured by ERs in 3D synthetic space.

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Data availability

The data that support the findings of this study are available via Zenodo at https://doi.org/10.5281/zenodo.13582346 (ref. 51). Source data are provided with this paper.

Code availability

The MATLAB codes for drawing the figures are available from the corresponding author upon reasonable request.

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Acknowledgements

Z.A. acknowledges financial support from the National Natural Science Foundation of China (Grant Nos. 11991060, 12027805, 12474042, 12174072 and 2021hwyq05), the Innovation Program for Quantum Science and Technology (Grant No. 2024ZD0300103), the Shanghai Science and Technology Committee (Grant No. 23DZ2260100) and the Sino-German Center for Research Promotion (Grant No. M-0174). Some of the experimental work was conducted in Fudan Nanofabrication Lab.

Author information

Author notes

  1. These authors contributed equally: Zejin Rao, Changhao Meng, Youcai Han.

Authors and Affiliations

  1. State Key Laboratory of Surface Physics, Institute of Nanoelectronic Devices and Quantum Computing, and Key Laboratory of Micro and Nano Photonics Structures (Ministry of Education) Department of Physics, Fudan University, Shanghai, China

    Zejin Rao, Changhao Meng, Youcai Han, Liping Zhu, Kun Ding & Zhenghua An

  2. Shanghai Branch, Hefei National Laboratory, Shanghai, China

    Zhenghua An

  3. Shanghai Key Laboratory of Metasurfaces for Light Manipulation, Shanghai, China

    Zhenghua An

  4. Yiwu Research Institute of Fudan University, Yiwu City, China

    Zhenghua An

  5. Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China

    Zhenghua An

Authors
  1. Zejin Rao
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Contributions

C.M., Z.R. and Y.H. conceived the idea. Z.R. and C.M. co-designed the experiments. Z.R. performed all the experiments with support from C.M. The theoretical framework with the effective Hamiltonians was established by C.M. together with Z.A. Z.R. and C.M. performed the data analysis and discussed the work with Z.A. and K.D. Z.A. wrote the paper with Z.R. and C.M. All authors commented on the paper. Z.A. supervised the whole project.

Corresponding author

Correspondence to Zhenghua An.

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Nature Physics thanks Giuseppe Maruccio and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

This file contains Supplementary Parts 1–11, including notes on the theoretical details, a discussion and Figs. 1–14.

Source data

Source Data Fig. 1

Measured reflection spectrum and extracted eigenvalue point data produced by fitting.

Source Data Fig. 2

Eigenvalue point data and theoretical ELs.

Source Data Fig. 3

Complex eigenvalue bands corresponding to two cases of braiding and no braiding.

Source Data Fig. 4

Complex eigenvalue bands corresponding to three selected path loops used to represent the braid group.

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Rao, Z., Meng, C., Han, Y. et al. Braiding reflectionless states in non-Hermitian magnonics. Nat. Phys. 20, 1904–1911 (2024). https://doi.org/10.1038/s41567-024-02667-x

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