Finite size effects on topological interface states in one-dimensional scattering systems

TL;DR

This paper investigates how the finite size of one-dimensional scattering systems affects topological interface states, revealing their robustness and resonance behavior through complex analysis.

Contribution

It introduces an analysis of finite-sized 1D topological systems, highlighting the persistence and characteristics of interface states in open scattering configurations.

Findings

Interface modes emerge from band inversion near the Dirac point.

Localized interface modes are robust against size variations.

The complex resonance distribution characterizes the topological states.

Abstract

One-dimensional topological edge modes are usually studied considering the interface between two different semi infinite periodic crystals (PCs) with inverted band structure around the Dirac point. Here we consider the case where the two PCs are finite, constituting an open scattering system, and we study the influence of the size of this finite structure on the interface mode by inspecting the complex resonances. First we show the complex resonance distribution corresponding to the band inversion around the Dirac point. Perturbations from the Dirac point display the emergence of the localized interface mode. We also report on a remarkable robustness of the interface mode as the system size varies which persists even for the smallest possible size.