Influence of (N,H)-terminated surfaces on stability, hyperfine structure, and zero-field splitting of NV centers in diamond

We present a density functional theory analysis of the negatively charged nitrogen-vacancy (${\mathrm{NV}}^{\ensuremath{-}}$) defect complex in diamond located in the vicinity of (111)- or (100)-oriented surfaces with mixed (N,H)-terminations. We assess the stability and electronic properties of the ${\mathrm{NV}}^{\ensuremath{-}}$ center, and we study their dependence on the H:N ratio of the surface termination. The formation energy, the electronic density of states, the hyperfine structure, and the zero-field-splitting parameters of an ${\mathrm{NV}}^{\ensuremath{-}}$ center are analyzed as a function of its distance and orientation to the surface. We find stable ${\mathrm{NV}}^{\ensuremath{-}}$ centers with bulklike properties at distances of at least $\ensuremath{\sim}8$ \AA{} from the surface provided that the surface termination consists of at least 25% substitutional nitrogen atoms. The studied surface terminations have a minor effect on the ground-state properties, whereas the NV orientation has major effects. Our results indicate that axial NV centers near a flat 100% N-terminated (111) surface are the optimal choice for NV-based quantum sensing applications as they are the least influenced by the proximity of the surface.