Topological bound states in the continuum

Abstract: Bound states in the continuum, originally proposed within the framework of quantum mechanics, have since been observed in a variety of physical contexts, including electromagnetism, acoustics, and optics. Of particular interest are those bound states in the continuum that are protected by continuous symmetries, as their stability makes them resistant to structural imperfections and material disorder. In this study, we demonstrate the existence of topologically protected bound states in the continuum by coupling a finite Su-Schrieffer-Heeger (SSH) chain to a metallic lead. These states are characterized by distinct features in the electrical response of the system, serving as a direct indication of their topological origin. The inherent robustness of such topologically protected states highlights their potential applications in fault-tolerant quantum information processing as well as in the design of advanced electronic and photonic devices.