ROBUST ELECTRONIC-NUCLEAR NV–¹³C SPIN SYSTEMS IN THE DIAMOND FOR QUANTUM TECHNOLOGIES

Using the methods of computational chemistry, we calculated matrices A_KL describing hyperfine interactions (HFI) between the electron spin of the color ‘nitrogen-vacancy’ center (NV center) in a diamond and a ¹³C nuclear spin located somewhere in the Н-terminated carbon cluster C₅₁₀[NV]H₂₅₂ hosting the NV center. The rates W₀ of the ¹³C spin flip-flops induced by anisotropic HFI are calculated systematically for all possible locations of ¹³C in the cluster. It is shown that in the cluster, there are specific positions of nuclear ¹³C spin, in which it almost does not undergo such flip-flops due to small off-diagonal elements in corresponding matrices A_KL. Spatial locations of the ¹³C stability positions in the cluster are discovered and characteristic splitting values in the spectra of optically detected magnetic resonance (ODMR) for the stable NV–¹³C systems are calculated, which can be utilized to identify them during their experimental search for use in emerging quantum technologies. It is shown that the positions of the ¹³C nuclear spin located on the NV center symmetry axis are completely stable (W₀ = 0). The characteristics of eight ‘axial’ NV–¹³C systems are elucidated. The presence of additional ‘non-axial’ near-stable NV–¹³C spin systems also exhibiting very low flip-flop rates (W₀ → 0) due to a high local symmetry of the spin density distribution resulting in vanishing the off-diagonal HFI matrix A_KL elements for such systems is revealed for the first time. Spatially, these ‘non-axial’ stable NV–¹³C systems are located near the plane passing through the vacancy of the NV center and being perpendicular to the NV axis. Analysis of the available publications showed that apparently, some of the predicted stable NV–¹³C systems have already been observed experimentally.

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