Interplay of Long-Range Hopping and Spatially Correlated Bond Disorder in the Topological Robustness of the Extended SSH Model

We investigate the robustness of topological edge states in the Su-Schrieffer-Heeger (SSH) model extended with next-nearest-neighbor (NNN) hopping, under the influence of spatially correlated bond disorder. While uncorrelated (white) disorder is known to degrade topological invariants rapidly, we demonstrate that correlated disorder induces a resonant protection mechanism when the correlation length matches the hopping scales. By analyzing the real-space winding number and the inverse participation ratio (IPR) across finite-size scaling, we map out a phase diagram revealing regimes where topology survives beyond the standard Anderson localization limit. Our results suggest that engineering correlation in disorder can be a viable strategy to stabilize topological phases in noisy experimental platforms such as photonic lattices.