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Bound States in the Continuum as Nodal Chain Points of Scattering Matrices

Wenzhe Liu1,2,3,*,†, Yuan-Song Zeng4,†, Jingyi Zhao1,2,†, Chenfeng Yang4, Ruo-Yang Zhang3, Xiaohan Cui3, Geng-Bo Wu4,‡, and C. T. Chan3,§

  • 1Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Songhu Road, Yangpu District, Shanghai 200438, China
  • 2State Key Laboratory of Surface Physics, Key Laboratory of Micro- and Nano-Photonic Structures (Ministry of Education), and Department of Physics, Fudan University, Songhu Road, Yangpu District, Shanghai 200438, China
  • 3Department of Physics and Institute for Advanced Study, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong 999077, China
  • 4State Key Laboratory of Terahertz and Millimeter Waves and Department of Electrical Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong 999077, China

  • *Contact author: wzliu@fudan.edu.cn
  • †These authors contributed equally to this work.
  • ‡Contact author: bogwu2@cityu.edu.hk
  • §Contact author: phchan@ust.hk
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Phys. Rev. Lett. 135, 243804 – Published 11 December, 2025

DOI: https://doi.org/10.1103/rpb2-ryyk

Abstract

Bound states in the continuum (BICs), exotic resonances with infinite lifetimes embedded in radiation continua, have long been studied for their topological robustness. Meanwhile, nodal lines—degenerate momentum-space manifolds in photonic and electronic band structures—represent another cornerstone of topological physics. Here, we unveil a profound connection between these phenomena by demonstrating that BICs act as topological chain points pinning together nodal lines within scattering-matrix eigenvalue space. Through scattering-matrix eigenphase analysis, we show that BICs enforce robust nodal chain formation in frequency-momentum space, even when system symmetries are broken. Experimentally, we validate this mechanism using a metasurface platform, where angle-resolved phase measurements reveal nodal lines intersecting at a symmetry-protected BIC. Strikingly, breaking mirror symmetry preserves the BIC-pinned nodal chain, highlighting its origin in the intrinsic singular scattering nature of BICs rather than conventional symmetry protection. This Letter establishes scattering matrices as a natural framework to unify BICs and nodal topology, offering new pathways to engineer topologically robust photonic systems resilient to perturbations. Our findings bridge fundamental concepts in topological photonics and open avenues for applications in metasurfaces and light-matter interaction control.

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Phys. Rev. Lett. 135, 243804– Published 11 December, 2025
  • Received 3 April 2025
  • Revised 30 October 2025
  • Accepted 19 November 2025
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