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Atomistic mechanism of perfect alignment of nitrogen-vacancy centers in diamond
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29. The ultrasoft pseudopotentials24,25 were adopted to represent the interactions between the valence electrons and ionic cores of all C, N, and H atoms. The wavefunctions were expanded in the plane-wave basis set up to the cut-off energy of 50 Ry. The augmentation charges of the ultrasoft pseudopotentials were also expanded in plane waves up to the cut-off energy of 320 Ry. The self-consistent-field (SCF) loops were iterated until the total energies of consecutive SCF steps was less than 1.5 × 10−6 eV/supercell, where the forces were calculated. The structure optimization was performed until the absolute values of all the components of all forces were smaller than 3 × 10−3 eV/Å.
30. We assumed that the upper and lower terrace C atoms in the α layers were mono-hydrogenated. In panel (a), one H atom was attached to the C atom at xk+1. In panel (b), we assumed that two H atoms were attached to the C atom at xk+2, whereas the one below the vacancy at xk+1 had an unpaired dangling bond.
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Nitrogen-vacancy (NV) centers in diamond have attracted a great deal of attention because of their possible use in information processing and electromagnetic sensing technologies. We examined the atomistic generation mechanism for the NV defect aligned in the  direction of C(111) substrates. We found that N is incorporated in the C bilayers during the lateral growth arising from a sequence of kink propagation along the step edge down to
. As a result, the atomic configuration with the N-atom lone-pair pointing in the  direction is formed, which causes preferential alignment of NVs. Our model is consistent with recent experimental data for perfect NV alignment in C(111) substrates.
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