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  • Open Access

Topological sound in nonreciprocal active-liquid networks

Minqi Cheng1,*, Jingming Chen1,*, Linyun Yang2,†, and Zhen Gao1,‡

  • 1State Key Laboratory of Optical Fiber and Cable Manufacturing Technology, Department of Electronic and Electrical Engineering, Guangdong Key Laboratory of Integrated Optoelectronics Intellisense, Southern University of Science and Technology, Shenzhen 518055, China
  • 2College of Aerospace Engineering, Chongqing University, Chongqing 400030, China

  • *These authors contributed equally to this work.
  • †Contact author: yanglinyun@cqu.edu.cn
  • ‡Contact author: gaoz@sustech.edu.cn
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Phys. Rev. Research 7, 043007 – Published 1 October, 2025

DOI: https://doi.org/10.1103/rvkr-7mr2

Abstract

Recent advances in nonreciprocal topological networks have discovered a type of anomalous topological edge states with superior robustness against larger disorders than the quasienergy band gap. However, to date, all previously demonstrated nonreciprocal topological networks have required external drives such as magnetic fields or time modulation to break the time-reversal symmetry (TRS). Here, by extending this concept to topological active matter systems with spontaneous TRS breaking, we demonstrate robust acoustic anomalous and Chern edge states in a self-propelled nonreciprocal active-liquid network without any external drives. More interestingly, we show that the anomalous topological edge states exhibit superior robustness against Hermitian disorders even than the Chern ones. Furthermore, we discover that such superior robustness no longer holds in the presence of non-Hermitian perturbations, and both the anomalous and Chern edge states transition to the corner skin modes by the non-Hermitian skin effect. Our work extends the nonreciprocal topological networks to active matter and non-Hermitian systems, offering possibilities for sound manipulation in a highly unusual way.

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Phys. Rev. Research 7, 043007– Published 1 October, 2025
  • Received 12 June 2024
  • Accepted 3 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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