Calculating the hyperfine tensors for group-IV impurity-vacancy centers in diamond using hybrid density functional theory
Rodrick Kuate Defo, Efthimios Kaxiras, Steven L. Richardson
Abstract
The hyperfine interaction is an important probe for understanding the structure and symmetry of defects in a semiconductor. Density functional theory has shown that it can provide useful first-principles predictions for both the hyperfine tensor and the hyperfine constants that arise from it. Recently there has been great interest in using group-IV impurity-vacancy color centers $\mathrm{X}{V}^{\ensuremath{-}}$ (where X = Si, Ge, Sn, or Pb and $V$ is a carbon vacancy) for important applications in quantum computing and quantum information science. In this paper we have calculated the hyperfine tensors for these $\mathrm{X}{V}^{\ensuremath{-}}$ color centers using the HSE06 screened Hartree-Fock hybrid exchange-correlation functional with the inclusion of core electron spin polarization. We have compared our results to calculations which only use the PBE exchange-correlation functional without the inclusion of core electron spin polarization and we have found that our results are in very good agreement with available experimental results. Finally, we have theoretically shown that these $\mathrm{X}{V}^{\ensuremath{-}}$ color centers exhibit a Jahn-Teller distortion which explains the observed anisotropic distribution of the hyperfine constants among the neighboring $^{13}\mathrm{C}$ nuclear spins.