Topological edge states and disorder robustness in one-dimensional off-diagonal mosaic lattices

TL;DR

This paper explores topological edge states in one-dimensional off-diagonal mosaic lattices, demonstrating their analytical existence, robustness against disorder, and potential for engineering multi-gap topological phases.

Contribution

It extends the SSH model to multi-band systems with periodic modulation and analyzes the robustness of edge states under disorder.

Findings

Edge states are analytically derived at specific energy levels.

Topological edge states are robust against off-diagonal disorder.

Fragile edge states appear for larger period  and are easily destroyed by disorder.

Abstract

We investigate topological edge states in one-dimensional off-diagonal mosaic lattices, where nearest-neighbor hopping amplitudes are modulated periodically with period $\kappa>1$. Analytically, we demonstrate that discrete edge states emerge at energy levels $E=\epsilon+2t\cos(\pi i/\kappa)$ ($i=1,\cdots,\kappa-1$), extending the Su-Schrieffer-Heeger model to multi-band systems. Numerical simulations show that these edge states are robustly localized and display characteristic nodal structures, with their existence being strongly dictated by the specific edge arrangement of long and short bonds. We further examine their stability under off-diagonal disorder, where the hopping amplitudes $\beta$ fluctuate randomly at intervals of $\kappa$. Using the inverse participation ratio as a localization measure, we show that these topological edge states remain robust over a broad range of disorder strengths. In contrast, additional $\beta$-dependent edge states that appear for $\kappa \ge 4$ are fragile and vanish even under relatively weak disorder. These findings highlight a rich interplay between topology, periodic modulation, and disorder, offering insights for engineering multi-gap topological phases and their realization in synthetic quantum and photonic systems.