First-principles theory of the luminescence lineshape for the triplet transition in diamond NV centres

Abstract

In this work we present theoretical calculations and analysis of the vibronic\nstructure of the spin-triplet optical transition in diamond nitrogen-vacancy\ncentres. The electronic structure of the defect is described using accurate\nfirst-principles methods based on hybrid functionals. We devise a computational\nmethodology to determine the coupling between electrons and phonons during an\noptical transition in the dilute limit. As a result, our approach yields a\nsmooth spectral function of electron-phonon coupling and includes both\nquasi-localized and bulk phonons on equal footings. The luminescence lineshape\nis determined via the generating function approach. We obtain a highly accurate\ndescription of the luminescence band, including all key parameters such as the\nHuang-Rhys factor, the Debye-Waller factor, and the frequency of the dominant\nphonon mode. More importantly, our work provides insight into the vibrational\nstructure of nitrogen vacancy centres, in particular the role of local modes\nand vibrational resonances. In particular, we find that the pronounced mode at\n65 meV is a vibrational resonance, and we quantify localization properties of\nthis mode. These excellent results for the benchmark diamond nitrogen-vacancy\ncentre provide confidence that the procedure can be applied to other defects,\nincluding alternative systems that are being considered for applications in\nquantum information processing.\n