Acta Optica Sinica (Online), Volume. 2, Issue 8, 0810001(2025)
Progress in Non-Abelian Band Topology in Photonics (Invited)
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
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)
CSTR:32394.14.AOSOL240473