Excited states of the negatively charged nitrogen-vacancy color center in diamond

Excited states of the negatively charged nitrogen-vacancy color center in diamond are studied using ab initio many-body perturbation theory (within $GW$ approximation and Bethe-Salpeter equation), including electronic exchange, correlation, and electron-hole interaction effects. We find that three singlets, one of which exhibits an intersystem crossing with the excited triplet, may be relevant for the fluorescence process in a way which has never been considered before. The calculated zero-phonon line for the visible excitation and that for the transition among the singlets are in good agreement with the experiments.

Figure 1

(Color online) Real-space distribution of the excited electron (red/gray) and hole (yellow/light gray) in the excited state ${}^{3}E$ of the NV center in diamond. N, C, and V denote the position of the nitrogen atom, the three-coordinated carbon atoms and the vacancy in the NV center, respectively.

Figure 2

The spin-polarized levels of the NV center in the ground state within DFT and GWA. The overbar in the wave function denotes down-spin electron. The valence-band maxima in both DFT and GWA are set to zero. CBM denotes the conduction-band minimum. Dotted arrows indicate excitations to the triplet and singlet excited states.

Figure 3

(a) Energy profiles of the NV center within $GW+\text{BSE}$ in the states ${{}^{3}A}_2$, ${}^{1}E$, ${{}^{1}A}_1$, ${}^{3}E$, and ${{}^{1}E}^{\prime }$ along the CDFT relaxation path in the state ${}^{3}E$, respectively. ISC denotes the intersystem crossing between the states ${}^{3}E$ and ${{}^{1}E}^{\prime }$. (b) Simplified energy-level diagram for the NV center. The solid, dotted, and dashed lines indicate radiative transitions, intersystem crossing transitions, and vibronic decays, respectively.