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

TL;DR

The paper addresses how the neutral SiV center in diamond responds magneto-optically to extreme isotropic strain, combining first-principles density-functional theory with a quadratic product Jahn-Teller framework to predict ZPL shifts, vibronic couplings, and spin–orbit behavior under hydrostatic pressures from roughly $-80$ to $180$ GPa. It shows that compression stiffens the lattice, reduces vibronic quenching, and substantially increases the Ham-reduced spin–orbit splitting, while isotropic tension above about $4\%$ breaks inversion symmetry and induces a tunneling-dominated, symmetry-lowered regime; charge stability constrains photoluminescence in the tensile regime. The authors provide compact calibration relations linking optical and spin observables to isotropic strain, establishing SiV0 as a symmetry-protected, strain-tunable quantum emitter that operates into multi-megabar conditions. These results advance high-pressure quantum metrology and diamond quantum photonics by offering a robust platform for strain-controlled, fiber-addressable quantum emitters.

Abstract

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.

Figures (5)

• Figure 1: (a) Atomic configuration of the SiV defect in diamond, consisting of a single silicon atom positioned between two adjacent carbon vacancies and coordinated by six neighboring carbon atoms (illustrated in blue, red, and black, respectively). (b) Electronic structure of the SiV triplet ground state. The red dashed arrow marks the electron excitation from the $e_u$ to the $e_g$ orbital, corresponding to the transition from $^3A_g$ to $^3E_u$. (c) Adiabatic potential energy surface (APES) of the quadratic product Jahn--Teller (pJT) system along the ionic coordinates. The instability energies, $E^i_{JT}$, are indicated for constructive ($i=1$) and destructive ($i=2$) interference of the two orbital branches. Axial asymmetry, a second-order effect, is described by the parameter $\Delta^i_{JT}$. (d) DFT-calculated potential energy surfaces along one-dimensional cuts. The $D_{3d}$ high-symmetry configuration (at 0.0 $\sqrt{\mathrm{amu}},\text{\AA}$) is unstable on two surfaces, in agreement with the pJT model. The splitting $\Lambda$ arises from static electronic correlation. Numerical values are provided in Table \ref{['tabale:PJT']}.
• Figure 2: (a) Adiabatic double-well potential $V(Q)$ along the mass-weighted distortion coordinate $Q$ ($\text{\AA}\sqrt{\mathrm{amu}}$), illustrating tensile-strain--induced symmetry breaking from the high symmetry $D_{3d}$ configuration at $Q=0$ to two symmetry equivalent low symmetry $C_{3v}$ minima at $Q=\pm Q_0$. The even-parity ground state $\psi_0$ and odd-parity first excited state $\psi_1$, with eigenenergies $E_0$ and $E_1$, are indicated by horizontal lines. Insets show the relaxed atomic structures at the $C_{3v}$ minima and at the $D_{3d}$ saddle point. (b) Schematic two-dimensional view of the adiabatic potential energy surface of SiV in the ground and excited states under $4\%$ tensile strain. The barrier energy $B_{\mathrm{gs/es}}$ denotes the energy difference between the $C_{3v}$ minima and the $D_{3d}$ saddle point in the ground/excited state, respectively.
• Figure 3: (a) Calculated charge transition levels of SiV defect under isotropic strain in the range of $-50$ to 180 GPa as obtained by HSE06 functional. (b) The ZPL shift was calculated by HSE06 functional. We highlight the strain regions by light red color where SiV is not photostable.
• Figure 4: Hyperfine parameters of the neutral SiV defect within the region of isotropic strain resulting in high $D_{3d}$ symmetry, showing $A_\parallel$ and $A_\perp$ in the ground state for (a) the dopant $^{29}$Si atom and (b) the first $^{13}$C neighbor atoms. The ground-state spin density is illustrated for (c) $-41.2$ GPa, (d) zero and (e) 180 GPa pressures. The spin density is defined as the charge-density difference between the majority and minority spin channels in spin-polarized calculations; the isosurface corresponds to positive spin density, with an absolute value of $0.02~\text{\AA}^{-3}$.
• Figure 5: Hyperfine parameters of the neutral SiV defect within the region of isotropic tensile strain resulting in low $C_{3v}$ symmetry, showing $A_\parallel$ and $A_\perp$ in the ground state for (a) the dopant $^{29}$Si atom and (b) the first $^{13}$C neighbor atoms that have two groups. The ground-state spin density is illustrated for (c) $-50.1$ GPa and (d) $-77.6$ GPa tensile strain. The spin density is defined as the charge-density difference between the majority and minority spin channels in spin-polarized calculations; the isosurface corresponds to positive (orange lobes) and negative (green lobes) spin density, with an absolute value of $0.006~\text{\AA}^{-3}$. The linear fitting in dashed lines is used to guide the eyes.