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

TL;DR

This paper investigates how bound states in the continuum (BICs) in a one-dimensional ladder-shaped photonic crystal induce topological states and flat bands, revealing new ways to engineer robust edge states and flat band phenomena.

Contribution

It introduces a novel analysis of BIC-induced topological states and flat bands in a ladder-shaped photonic crystal using band topology and symmetry considerations.

Findings

Topologically protected edge states with quantized Zak phase

Robust flat bands linked to symmetry-protected BICs

Mechanisms for topological band inversion and flat band formation

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.