Selection rules in the excitation of the divacancy and the nitrogen-vacancy pair in 4H- and 6H-SiC

In this study, we address selection rules with respect to the polarization of the optical excitation of two color centers in $4H\text{−}\mathrm{SiC}$ and $6H\text{−}\mathrm{SiC}$ with potential for applications in quantum technology, the divacancy and the nitrogen-vacancy pair. We show that the photoluminescence of the axial configurations of higher symmetry $\left(C_{3v}\right)$ than the basal ones $\left(C_{1h}\right)$ can be canceled using any excitation (resonant or nonresonant) with polarization parallel to the crystal axis $\left(E_L\left|\right|c\right)$. The polarization selection rules are determined using group-theoretical analysis and simple physical arguments showing that phonon-assisted absorption with $E_L\left|\right|c$ is prohibited despite being formally allowed by group theory. A comparison with the selection rules for the silicon vacancy, another defect with $C_{3v}$ symmetry, is also carried out. Using the selection rules, we demonstrate selective excitation of only one basal divacancy configuration in $4H\text{−}\mathrm{SiC}$, the PL3 line, and discuss the higher contrast and increased Debye-Waller factor in the selectively excited spectrum.