Magneto-optical properties of the neutral silicon-vacancy center in diamond under extreme isotropic strain fields

The neutral silicon–vacancy (SiV$^{0}$) center in diamond combines inversion symmetry with optical emission, making it a robust quantum emitter resilient to stray electric fields. Using first-principles density-functional theory, we quantify its response to isotropic strain spanning strong compression and tensile regimes (effective hydrostatic pressures of approximately $-80$ to $180$~GPa). The coexistence of doubly degenerate $e_g$ and $e_u$ levels produces a structural instability captured by a quadratic product Jahn–Teller model. Under isotropic compression, the zero-phonon line blue-shifts nearly linearly while the $E_g$ phonon stiffens, suppressing vibronic instabilities and reducing Jahn–Teller quenching. Consequently, the Ham-reduced excited-state spin–orbit splitting increases substantially and the dark–bright vibronic gap widens. In contrast, isotropic tensile strain enhances vibronic effects and induces symmetry breaking beyond a critical strain, with tunneling-mediated dynamical averaging at the onset. Throughout the symmetry-preserving regime, parity remains well defined, so isotropic strain alone does not activate the dark transition. Charge-transition levels indicate photostability of the emission deep into the compressive regime, and near the highest photostable deformation ($\sim 100$~GPa), the radiative lifetime increases due to a reduced transition dipole moment despite the increasing optical energy. These trends yield compact calibration relations linking optical and spin observables to isotropic strain and establish SiV$^{0}$ as a symmetry-protected, strain-tunable quantum emitter operating into the multi-megabar-equivalent regime.

💡 Research Summary

The neutral silicon‑vacancy (SiV⁰) defect in diamond combines inversion symmetry (D₃d) with a bright zero‑phonon line (ZPL) at 946 nm, making it intrinsically immune to linear Stark shifts. In this work the authors employ hybrid‑functional (HSE06) density‑functional theory on a 512‑atom supercell to explore how isotropic (hydrostatic) strain—from strong compression (≈ −80 GPa) to extreme tension (≈ +180 GPa, equivalent to up to 8 % tensile strain)—modifies the electronic, vibronic, and magnetic properties of SiV⁰.

The key electronic structure consists of doubly‑degenerate e_g and e_u orbitals. In the neutral charge state e_u is fully occupied while e_g is half‑filled, giving a spin‑triplet (S = 1) ground state (³A₂g). Optical excitation promotes an electron from e_u to e_g, generating an excited manifold that splits into ³E_u (bright) and ³A₂u (dark) components. Both e_g and e_u are Jahn–Teller (JT) active and couple to the same E_g phonon mode, forming a quadratic product JT (pJT) system of type E_g ⊗ e_u ⊗ e_g.

Under compression the E_g phonon stiffens (ℏω rises from ~80 meV to ~92 meV) and the ZPL blue‑shifts almost linearly (~0.8 meV GPa⁻¹). The JT stabilization energies (E₁_JT, E₂_JT) decrease, reducing the vibronic distortion. Consequently the Ham reduction factor λ diminishes, leading to a substantial increase of the excited‑state spin‑orbit splitting (Δ_SO grows by ~30 %). The dark‑bright vibronic gap δ also widens, improving optical purity.

In the tensile regime the opposite trend occurs. Beyond ≈ 4 % tensile strain (≈ −50 GPa) the high‑symmetry D₃d configuration becomes unstable, giving rise to a symmetric double‑well potential with two equivalent C₃v minima. The barrier height drops from 115 meV at 4 % strain to essentially zero at 8 % strain, and the tunneling splitting ΔE collapses from ~22 GHz to < 1 MHz. This dynamical averaging means that on fast experimental timescales the defect still appears D₃d‑symmetric, but on slower scales the C₃v distortion would be observable. Importantly, parity remains a good quantum number throughout the symmetry‑preserving regime, so pure isotropic strain cannot activate the dark ³A₂u transition (≈ 951 nm).

Charge‑transition level (CTL) calculations using the Freysoldt–Neugebauer–Van de Walle correction show that both (0/−1) and (0/+1) levels stay within the band gap throughout the whole pressure range, confirming photostability even under extreme compression. Near 100 GPa the transition dipole moment is reduced, leading to a longer radiative lifetime despite the higher transition energy.

The authors extract a set of pJT parameters (F_g, F_u, Λ, δ, Ξ) and fit simple linear or quadratic functions of pressure for experimentally accessible observables: ZPL energy, spin‑orbit splitting, tunneling rate, and CTLs. These calibration relations enable the SiV⁰ center to serve as a quantum pressure gauge or strain sensor operating up to multi‑megabar equivalent stresses.

Overall, the study demonstrates that SiV⁰ is a symmetry‑protected quantum emitter whose optical and spin properties can be tuned in opposite directions by compression versus tension: compression suppresses vibronic instability and enhances spin‑orbit coupling, while tension amplifies vibronic effects, induces a symmetry‑breaking double‑well, and slows tunneling. The robustness of the defect under both extreme compression and tensile strain, together with the derived calibration formulas, positions SiV⁰ as a promising platform for high‑pressure quantum metrology, strain‑engineered photonics, and resilient solid‑state qubits.