Engineering Quantum Phases in Two Dimensions via Vacancy-Induced Electronic Reconstruction

Abstract: Topological phases of matter are commonly understood as emerging either from crystalline symmetry and intrinsic spin-orbit coupling or from disorder-driven electronic renormalization. In realistic materials, however, structural defects naturally combine both ingredients. Here, we demonstrate a general and material-independent mechanism by which atomic vacancies can induce topological phase transitions in two-dimensional semiconductors that are otherwise topologically trivial. Vacancies generate locally ordered dangling-bond states governed by well-defined hopping and spin-orbit interactions, while their spatial distribution and mutual coupling introduce long-range disorder. As vacancy concentration increases, the hybridization of these defect states forms an emergent electronic subspace that undergoes a topological transition. Using a tight-binding framework supported by large-scale density functional theory calculations, we show that this vacancy-induced electronic reconstruction can robustly stabilize quantum spin Hall, quantum anomalous Hall, and Weyl semimetal phases, depending on symmetry breaking and spin polarization. Our results establish vacancies not merely as perturbations, but as active design elements capable of transforming trivial insulators into topological quantum matter, opening realistic routes for defect-engineered topological devices.