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  • Open Access

General theory for nonzero subsymmetry-protected topological chiral boundary states

Yunlin Li, Yufu Liu, Xuezhi Wang, Haoran Zhang, and Xunya Jiang*

  • Department of Illuminating Engineering and Light Sources, College of Intelligent Robotics and Advanced Manufacturing, Fudan University, Shanghai 200433, China

  • *Contact author: jiangxunya@fudan.edu.cn
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Phys. Rev. Research 8, 013256 – Published 9 March, 2026

DOI: https://doi.org/10.1103/86m4-lds2

Abstract

Symmetry plays an important role in the topological band theory. Recently, the concept of subsymmetry-protected topological (sub-SPT) phases [Nat. Phys. 19, 992 (2023)] suggests that chiral edge states can exist in a system with broken symmetry. However, sub-SPT theory only focuses on the zero-energy edge states in the half-filling gap, which limits its application. In this work, we extend the scope of sub-SPT phases in both one-dimensional (1D) and two-dimensional (2D) multigap asymmetric systems through redefined sublattices. In three typical asymmetric models without subsymmetry, we find that all the nonzero edge (corner) states can be illustrated by sub-SPT chiral edge (corner) states after redefining sublattices. Moreover, these nonzero chiral boundary states can exhibit some exotic properties, such as the topological bound states in the continuum. As to the bulk-edge correspondence, a universal topological invariant Z¯ is defined, which can precisely predict the appearance of chiral boundary states in both 1D and 2D systems. Finally, we propose an acoustic experiment where the nonzero chiral corner states are numerically observed. Our work exhibits a general approach to study the topological properties of asymmetric systems, opening up possibilities for topological phenomena.

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Phys. Rev. Research 8, 013256– Published 9 March, 2026
  • Received 23 October 2025
  • Accepted 17 February 2026
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