Construction of Topological Bound States in the Continuum Via Subsymmetry.

Topological bound states in the continuum (BICs) are localized topological boundary modes coexisting with a continuous spectrum of extended modes. They have been realized in systems with symmetry-protected topological phases, where their immunity to defects and perturbations depends on the presence of symmetries. Here we propose a method that transforms an in-gap topological boundary state into a BIC by using the concept of subsymmetry. We design the coupling between a system possessing in-gap topological modes and a system possessing a continuum of states that results in topological BICs. We define the criteria for the coupling that yields the desired results. To implement this scheme, we construct representative topological BICs based on one-dimensional Su-Schrieffer-Heeger models and implement them in photonic lattices. Our results not only reveal novel physical phenomena but may also provide methods for designing a new generation of topological devices.