Abstract
We present a many-body perturbation theory study of the excitonic properties of wurtzite GaN containing a single charged nitrogen vacancy. We determine that the lowest-energy exciton consists of a bulk to defect transition, resulting in a slight redshift ($<0.1$ eV) of the optical absorption onset and a 50 meV increase in the exciton binding energy when compared with pristine bulk. Furthermore, by analysis of the electron-hole correlation function, we quantify the defect-induced localization of the Wannier-Mott exciton in two ways. First, we show that the electron-hole separation is reduced, and that the exciton envelope wave function can be related to a simple model of a defect-bound exciton. Second, we show that the exciton center-of-mass does not display the periodicity of the lattice due to defect-induced localization. We anticipate that our approach, which quantitatively describes the influence of a point defect on the exciton wave function, will be generally applicable.
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