Acta Optica Sinica (Online), Volume. 2, Issue 8, 0810001(2025)

Progress in Non-Abelian Band Topology in Photonics (Invited)

Changze Li1...2,3, Zhanshan Wang1,2,3, Xinbin Cheng1,2,3, and Tianshu Jiang1,23,* |Show fewer author(s)
Author Affiliations
  • 1Institute of Precision Optical Engineering, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
  • 2MOE Key Laboratory of Advanced Micro-Structured Materials, Shanghai 200092, China
  • 3Shanghai Frontiers Science Center of Digital Optics, Shanghai 200092, China
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    Non-Abelian band topology is a recently proposed topological theory used to describe the topological properties of multi-band systems with space-time inversion symmetry. By drawing an analogy to defects in liquid crystal molecules, it is discovered that the non-Abelian topological charge in multi-band systems can be described using quaternions and generalized quaternions. Since this topological description involves multiple band gaps, the corresponding edge state distribution becomes more complex. Currently, non-Abelian band topology theory is primarily used to explain and describe the violation of the Nielsen?Ninomiya theorem, allowed nodal line configurations, braiding of nodal lines, and path-dependent nodal point collisions. In addition, the Euler number used to characterize the topological properties of triple degenerate points is also related to the non-Abelian topological charge and has been widely applied in the study of nodal lines. In this paper, we begin with the fundamental theory of non-Abelian band topology, systematically review the unique physical phenomena predicted by this theory in photonic and other systems, introduce the latest experimental observations, and further explore the future development prospects of this field.

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    Changze Li, Zhanshan Wang, Xinbin Cheng, Tianshu Jiang. Progress in Non-Abelian Band Topology in Photonics (Invited)[J]. Acta Optica Sinica (Online), 2025, 2(8): 0810001

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    Paper Information

    Category: Topological Photonics

    Received: Dec. 16, 2024

    Accepted: Feb. 10, 2025

    Published Online: Apr. 10, 2025

    The Author Email: Jiang Tianshu (tsjiang@tongji.edu.cn)

    DOI:10.3788/AOSOL240473

    CSTR:32394.14.AOSOL240473

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