Ab-initio photoluminescence spectrum of NV⁻ centres by Time-Dependent Density Functional Theory

Quantum information and communication require single photons on demand, however current state of the art emitters are probabilistic. Defect centres in nanomaterials have shown promise as deterministic single photon sources. To investigate these materials, first principle models are required. Purely Density Functional Theory (DFT) models have met with much success, however, DFT is a ground state theory and excited states can only be calculated under strict assumptions. Here we demonstrate a method to calculate the ab-initio photoluminescence spectrum for NV^- centres using Time-Dependent Density Functional Theory (TD-DFT). Ground state properties are calculated using DFT. Excited state energies and transition dipole moments are calculated with Linear Response TD-DFT. Excited vibrational modes are given as normal modes the TD-DFT energy second derivatives. The emission rate is calculated from the transition dipole moment and Franck-Condon overlaps. Our technique can be extended to more general defects and is especially useful for edge effects like with small clusters or defects with Jahn-Tellar distortions. The ability to recreate experimental photoluminescence spectra marks a step forward in understanding and controlling single photon emission for defect emitters.