Multimode Jahn-Teller Effect in Negatively Charged Nitrogen-Vacancy Center in Diamond

We present a first-principles study of the multimode Jahn-Teller (JT) effect in the exctied $^{3}E$ state of the negatively charged nitrogen-vacancy (NV) center in diamond. Using density functional theory combined with an intrinsic distortion path (IDP) analysis, we resolve the full activation pathways of the JT distortion and quantitatively decompose the distortion into contributions from individual vibrational modes. We find that multiple vibrational modes participate cooperatively in the JT dynamics, giving rise to a shallow adiabatic potential energy surface with low barriers, consistent with thermally activated pseudorotation. The dominant JT-active modes are found to closely correspond to vibrational features observed in two-dimensional electronic spectroscopy (2DES), in agreement with recent ab initio molecular dynamics simulations. Our results establish a microscopic, mode-resolved picture of vibronic coupling in the excited-state NV center and provide new insight into dephasing, relaxation, and optically driven dynamics relevant to solid-state quantum technologies.

💡 Research Summary

This paper presents a comprehensive first‑principles investigation of the multimode Jahn‑Teller (JT) effect in the optically excited ^3E state of the negatively charged nitrogen‑vacancy (NV⁻) center in diamond. Using density‑functional theory (DFT) with the screened hybrid functional HSE06 and the intrinsic distortion path (IDP) methodology, the authors map the full adiabatic potential energy surface (APES) connecting the high‑symmetry C₃ᵥ configuration to the low‑symmetry C₁ʰ minima. The calculated JT stabilization energy at the minima is 41 meV, while the barrier separating adjacent minima is only 9.9 meV, indicating a shallow landscape that permits near‑free pseudorotation at room temperature.

The IDP analysis treats the low‑symmetry minimum as a reference and expresses any distortion as a linear combination of all normal modes of that minimum. By constructing a total harmonic force as a weighted sum of mode‑specific forces, the authors generate a physically realistic relaxation pathway from the high‑symmetry saddle point to the minimum. This pathway is steeper than the straight‑line “direct path” (DP), showing that the system stabilizes more efficiently when the collective mode forces are considered.

A quantitative mode‑decomposition reveals that many vibrational modes contribute appreciably to the JT distortion. For the transition from the high‑symmetry point to the minimum, three a₁ modes at 45.0 meV, 57.8 meV, and 64.0 meV dominate, accounting for roughly 31 %, 30 %, and 9 % of the total distortion, respectively. In the reverse transition from the saddle point to the minimum, modes at 31.6 meV, 46.5 meV, and 57.3 meV are most important, contributing 44 %, 17 %, and 9 % respectively. In total, 36–42 modes exceed a 0.25 % contribution threshold, together representing about 87 % of the total geometric change and roughly 65 % of the JT stabilization energy.

Crucially, the energies of the dominant JT‑active modes fall within the 30–65 meV range observed in recent two‑dimensional electronic spectroscopy (2DES) experiments on NV⁻ centers. This correspondence provides a direct link between the multimode JT picture and experimentally measured vibronic features, resolving discrepancies that single‑mode models could not explain.

The authors also discuss the limitations of a purely harmonic treatment. While the harmonic IDP reproduces the overall shape of the APES, it overestimates the barrier height (≈30 meV) compared with the full DFT value (≈10 meV), highlighting the importance of anharmonicity in softening the potential surface. This anharmonic contribution is essential for accurately describing the low‑energy dynamics and the temperature‑dependent pseudorotation.

Overall, the study delivers a mode‑resolved microscopic understanding of vibronic coupling in the NV⁻ excited state. By demonstrating that multiple phonon modes cooperate to produce a shallow JT landscape, the work clarifies the origins of optical dephasing, spin‑relaxation, and photon depolarization observed experimentally. These insights are directly relevant to the design of NV‑based quantum sensors, photonic devices, and solid‑state quantum information platforms, where control over electron‑phonon interactions is pivotal for improving coherence times and operational fidelity.