Electronic-Structure Model for a Single Vacancy Defect

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Abstract
We propose a first-principles electronic structure model for describing a single vacancy defect. Vacancy defects in semiconductors and insulators form color centers, whose localized trap states enable quantum functionalities. The properties of these defect states are affected by their interactions with the surrounding lattice and spin environments. Extensive theoretical efforts have been devoted to understanding such defect-environment couplings within periodic supercell models. While these approaches have provided valuable insights, accurate description of charged defects or nuclear motion associated with electron-phonon coupling requires approaching the dilute-defect limit, which in turn demands prohibitively large supercells and computational cost. Our new model eliminates the artificial periodicity inherent to the supercell model. A single defect is introduced into the pristine crystal under the assumption that the electronic density far from the defect remains nearly identical to that of the pristine system. For the insulating LiH-1D system, this assumption holds well, as neutral and charged defects form localized color centers consistent with the model. In contrast, for the metallic H-1D system, delocalized electronic behavior in charged defects violates this locality condition, limiting the applicability of the approach. We expect that this model can be broadly applicable to investigations of charged color centers and their interactions with the surrounding environment in insulating and semiconducting materials such as diamond, h-BN, transition-metal oxides, and dichalcogenides.

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