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arXiv · 2603.17830

Topological states and flat bands induced by bound states in the continuum in a ladder-shaped one-dimensional photonic crystal

Sofía Pinto·P. A. Orellana·Sergio Bravo
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Abstract

One-dimensional crystals serve as a versatile platform for engineering nontrivial states, which can be easily explored in transport configurations. In this work, we analyze the properties of a periodic structure composed of an H-shaped unit cell, which forms a periodic ladder-shaped system. Using tight-binding models, group-theoretical considerations, and standard band topology, we uncover the influence of bound states in the continuum (BICs) and quasi-BICs formed in the original finite geometry on the creation of nontrivial band states. By designing various textures for the onsite energies, we discovered a topological band inversion between quasi-BIC-induced bands, leading to the emergence of topologically protected edge states that are characterized by a quantized Zak phase. Additionally, we found an on-site configuration that exhibits robust flat bands, induced by a symmetry-protected BIC and linked to special one-sided localized edge states. We present a detailed analysis of the mechanisms driving both effects and discuss the crucial role of symmetry in characterizing the topological phases of these systems.

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Sofía Pinto, P. A. Orellana, Sergio Bravo. 2026-03-18. Topological states and flat bands induced by bound states in the continuum in a ladder-shaped one-dimensional photonic crystal. https://arxiv.org/abs/2603.17830

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