The negatively charged silicon vacancy (SiV) color center in diamond has recently proven its suitability for bright and stable single photon emission. However, its electronic structure so far has remained elusive. We here explore the electronic structure by exposing single SiV defects to a magnetic field where the Zeeman effect lifts the degeneracy of magnetic sublevels. The similar responses of single centers and a SiV ensemble in a low strain reference sample prove our ability to fabricate almost perfect single SiVs, revealing the true nature of the defect's electronic properties. We model the electronic states using a group-theoretical approach yielding a good agreement with the experimental observations. Furthermore, the model correctly predicts polarization measurements on single SiV centers and explains recently discovered spin selective excitation of SiV defects.

Defect levels are a problem for standard implementations of density-functional theory and the error also influences the energetics. We demonstrate that the HSE06 functional, which describes the electronic structure of all group-IV semiconductors well (including Ge), gives highly accurate charge transition levels, too, if the defect wave function is host related\char22{}independent of localization. The degree of fulfilling the generalized Koopmans' theorem shows the reliability of the results and the highest-occupied eigenvalue always seems to give the correct vertical ionization energy.