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Abstract
The multimode Jahn-Teller (JT) effect in a bulk system of a neutral nitrogen-vacancy ($\mathrm{N}{\mathrm{V}}^{0}$) center in diamond is investigated via first-principles density-functional-theory calculations and the intrinsic distortion path (IDP) method. The adiabatic potential energy surface of the electronic ground state of the $\mathrm{N}{\mathrm{V}}^{0}$ center is calculated based on the local spin-density approximation. Our calculations confirm the presence of the dynamic Jahn-Teller effect in the ground $^{2}E$ state of the $\mathrm{N}{\mathrm{V}}^{0}$ center. Within the harmonic approximation, the IDP method provides the reactive path of JT distortion from unstable high-symmetry geometry to stable low-symmetry energy minimum geometry, and it describes the active normal modes participating in the distortion. We find that there is more than one vibrational mode contributing to the distortion, and their contributions change along the IDP. Several vibrational modes with large contributions to JT distortion, especially those modes close to 44 meV, are clearly observed as the phonon sideband in photoluminescence spectra in a series of experiments, indicating that the dynamic Jahn-Teller effect plays an important role in the optical transition of the $\mathrm{N}{\mathrm{V}}^{0}$ center.
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