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.

Figures (5)

• Figure 1: Vacancy interaction model and topological phase transition. (a) Schematic of vacancy local environment, where the DBS are highlighted in purple. Arrows indicate the intra-vacancy hopping $t$ and spin-orbit coupling $\lambda$ within the ordered local host, alongside the inter-vacancy coupling $t'$ that governs long-range interactions. (b) Fraction of systems presenting non-trivial topology, where $N$ represents the number of sites for each vacancy environment. (c) Eigenstates evolution for increasing value of inter-vacancy interaction. The DOS plot for all the 1000 systems together, with $N_k$ the total number of k-points. The color os the DOS states are related to the accumulated phase over a cyclic evolution in the vacancy environment (see Methods).
• Figure 2: Topological phase interpretation (a) Hamiltonian terms for lower (left) and higher (right) inter-vacancy interaction $t'$. (b) Accumulate phase over cyclic evolution. (c) Eigenstates and respective accumulated phase (color) for different local vacancy environment.
• Figure 3: High-throughput screening and topological phase classification. (a) Computational workflow for the identification of candidate 2D semiconductors from the C2DB database. (b) Selection criteria used to filter the database, including pristine bandgap, magnetic ground state, and thermodynamic stability. This filtering identified 308 host materials, which were systematically expanded into 768 symmetry-unique vacancy configurations, as shown in (c). (d) Distribution of the vacancy-induced states relative to the host bandgap; out of the 235 systems with isolated defect bands, 164 exhibit a density of states pinned at the Fermi level. (e) Schematic representation of the universal topological phase screening. The trajectories illustrate the emergence of Weyl semimetal (WSM), quantum anomalous Hall (QAH), and quantum spin Hall (QSH) phases as a function of vacancy density and symmetry-breaking parameters.
• Figure 4: Topological phase driven by vacancy. (a) Quantum spin Hall, (b) Quantum anomalous Hall, and (c) Weyl semimetal phase panels. Their respective chosen Vacancy structures are HgI (a-1), GeS$_2$ (b-1) and AgI (c-1) systems, with their corresponding band structures in low [(a-2), (b-2) and (c-2)] and medium [(a-3), (b-3) and (c-3)] vacancies concentration. The vacancy sites are indicated by red dashed circles. By increasing the vacancy concentration, the topological phase transition can be noted, as schematically shown in (a-4) and (b-4). The Weyl semimetal phase is a critical transition point, with a delta peak Berry curvature in Weyl points position (c-4). Due to bulk boundary-correspondence, spin-polarized topological edge states emerge connecting the bands with gap open by SOC in bulk (a-5) and (b-5). The topological edge states for WSM is shown in (c-5).
• Figure 5: Critical vacancy density as a function of the $t'/\lambda$ value for different vacancy systems, as indicated in the legend box inset. Here, we employ the C2DB notation to name different structures with same atomic configuration. The critical region for the topological phase transition is marked in light blue.