{\sigma}h-Broken Induced Topological quasi-BIC

Transitions from bound states in the continuum (BICs) to quasi-BICs (qBICs) are typically realized by introducing in-plane asymmetry, including permittivity asymmetry ({\epsilon}-qBICs) and geometry asymmetry (g-qBICs). Here, we demonstrate that when the in-plane symmetry is rigorously kept, the transition can also be occurred, provided the out-of-plane asymmetry is designed, which is called {\sigma}h -qBICs in this work. When the {{\sigma}h symmetry is gradually broken, the system undergoes a topological phase transition characterized by a Zak phase inversion, leading to a band inversion between quadrupole and dipole modes. This process not only enables controlled radiation coupling of BICs but also introduces a defect-immune qBIC regime. Our findings establish a general mechanism for engineering high-Q resonances and topologically robust plasmonic cavities.