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We present a theoretical study of vibrational and vibronic properties of a point defect in the dilute limit by means of first-principles density functional theory calculations. As an exemplar we choose the negatively charged nitrogen-vacancy (NV) center, a solid-state system that has served as a testbed for many protocols of quantum technology. We achieve low effective concentrations of defects by constructing dynamical matrices of large supercells containing tens of thousands of atoms. The main goal of the paper is to calculate luminescence and absorption lineshapes due to coupling to vibrational degrees of freedom. The coupling to symmetric a 1 modes is computed via the Huang-Rhys theory. Importantly, to include a nontrivial contribution of e modes we develop an effective methodology to solve the multimode E ⊗ e Jahn-Teller problem. Our results show that for NV centers in diamond a proper treatment of e modes is particularly important for absorption. We obtain good agreement with experiment for both luminescence and absorption. Finally, the remaining shortcomings of the theoretical approach are critically reviewed. The presented theoretical approach will benefit identification and future studies of point defects in solids.

Silicon-vacancy (SiV) center in diamond is a photoluminescence (PL) center with a characteristic zero-phonon line energy at 1.681 eV that acts as a solid-state single photon source and, potentially, as a quantum bit. The majority of the luminescence intensity appears in the zero-phonon line; nevertheless, about 30% of the intensity manifests in the phonon sideband. Since phonons play an essential role in the operation of this system, it is of importance to understand the vibrational properties of the SiV center in detail. To this end, we carry out density functional theory calculations of dilute SiV centers by embedding the defect in supercells of a size of a few thousand atoms. We find that there exist two well-pronounced quasi-local vibrational modes (resonances) with A2u and Eu symmetries, corresponding to the vibration of the Si atom along and perpendicular to the defect symmetry axis, respectively. Isotopic shifts of these modes explain the isotopic shifts of prominent vibronic features in the experimental SiV PL spectrum. Moreover, calculations show that the vibrational frequency of the A2u mode increases by about 30% in the excited state with respect to the ground state, while the frequency of the Eu mode increases by about 5%. These changes explain experimentally observed isotopic shifts of the zero-phonon line energy. We also emphasize possible dangers of extracting isotopic shifts of vibrational resonances from finite-size supercell calculations, and instead propose a method to do this correctly.

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