2026/07/27 by Sofia Pinto, Pedro A Orellana, S Bravo
paper · doi:10.1088/1402-4896/ae913c
Abstract One-dimensional crystals serve as a versatile platform for engineering nontrivial states that
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, forming 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 discover a topological band
inversion between quasi-BIC-induced bands, leading to the emergence of topologically protected
edge states characterized by a quantized Zak phase. Additionally, we identify an onsite
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.