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

Sofía Pinto, P. A. Orellana외 1명|arXiv (Cornell University)|2026. 03. 18.

Topological Materials and Phenomena인용 수 0

한 줄 요약

본 논문은 bound states in the continuum (BICs)와 quasi-BICs가 사다리형 1D 광결정에서 위상 밴드와 평탄 밴드를 생성하는 방식과, tight-binding, symmetry, 및 Zak phase 계산을 통해 분석하고, 벌크-경계 대응이 경계 상태를 확인한다.

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.

연구 동기 및 목표

• Explore how BICs and quasi-BICs in a ladder-shaped 1D photonic crystal influence band topology.
• Demonstrate band inversion and topological transitions induced by intercell hopping and onsite detuning.
• Characterize Zak phases and their symmetry protection across different two-color Frieze groups.
• Identify conditions leading to flat bands and symmetry-protected edge states.
• Validate bulk-boundary correspondence via finite-system spectra and LDOS analyses.

제안 방법

• Construct a one-dimensional periodic ladder-shaped unit cell with central chain and four arms.
• Use tight-binding models with parameters t_a, t_c, t_i and onsite energies ε_0, ε_{a_i_j}; set ε_0 = 0 and study cases with |ε| controls.
• Classify configurations with two-color Frieze groups: P2′m′m, P2m′m′, P2′mm′, via combined symmetry CX.
• Compute band structures, identify BIC- and quasi-BIC-induced bands, and track band inversions as t_i varies.
• Compute Zak phase for nondegenerate bands to diagnose topological phases and relate to symmetry protections.
• Analyze flat bands arising from mirror anti-symmetric bound states in the P2′mm′ group.
• Perform finite-system spectra and LDOS to illustrate bulk-boundary correspondence and edge-state localization.

실험 결과

연구 질문

• RQ1 How do BICs and quasi-BICs from the unit cell create bands in the periodic ladder-shaped crystal?
• RQ2 What is the mechanism and parameter dependence of topological band inversion induced by intercell hopping (t_i) and onsite detuning (|ε|)?
• RQ3 How do Zak phases behave under different two-color Frieze group symmetries and what symmetry protections quantize them?
• RQ4 Under which conditions do flat bands arise, and what is their relation to mirror symmetry?
• RQ5 Do finite systems exhibit bulk-boundary correspondence and edge states tied to the topological bands?

주요 결과

• A band inversion between quasi-BIC-induced bands signals a topological transition controlled by t_i (and dependent on |ε|).
• Zak phase is quantized (0 or π) for P2′m′m and P2m′m′ groups, indicating topological phases protected by M_y or inversion, respectively, while P2′mm′ yields non-quantized Zak phases.
• Finite systems show protected edge states in the nontrivial phase for P2′m′m, confirming bulk-boundary correspondence; edge states resemble SSH-like states.
• P2′mm′ supports flat bands arising from mirror anti-symmetric bound states due to M_x symmetry; such flat bands are absent in the other two groups.
• Topological edge states do not couple to the continuum in two-lead transport simulations, consistent with bound-state in the continuum (BIC) nature.