Magneto-optical properties of Group-IV--vacancy centers in diamond upon hydrostatic pressure

TL;DR

This work provides a first-principles, pressure-dependent map of magneto‑optical properties for negatively charged group-IV–vacancy centers in diamond (SiV, GeV, SnV, PbV). By combining plane-wave DFT with Jahn–Teller dynamics and a Jahn–Teller–aware hyperfine framework, the authors compute how ZPLs, photoionization thresholds, spin–orbit couplings, hyperfine interactions, and Zeeman responses evolve under hydrostatic pressures up to $180\ \text{GPa}$. The study reveals a dopant‑dependent deformation-potential hierarchy, identifies a 32 GPa limit for PbV$^{-}$ photostability, and provides pressure‑dependent estimates of electron spin coherence times, all with implications for in situ high‑pressure quantum sensing. The results establish bounding benchmarks and a theoretical toolkit for interpreting pressure‑tuned magneto‑optical signals in G4V centers, enabling calibrated sensing under extreme conditions and comparison with NV centers.

Abstract

In recent years, the negatively charged group-IV--vacancy defects in diamond, labeled as G4V(-) or G4V centers, have attracted significant attention in quantum information processing. In this study, we investigate the magneto-optical properties of G4V centers under high compressive hydrostatic pressures up to 180 GPa. The spin-orbit splitting of the electronic ground and excited states, as well as the hyperfine tensors, are calculated using plane-wave supercell density functional theory, providing distinctive fingerprints that uniquely characterize these defects. To this end, we develop a theory for calculating the hyperfine tensors when the electronic states are subject to the Jahn--Teller effect. We find that the zero-phonon-line energy increases with hydrostatic pressure, with the deformation potential increasing from SiV(-) to PbV(-). On the other hand, our calculated photoionization threshold energies indicate that PbV(-)-based quantum sensors can operate only up to 32 GPa, whereas SnV(-), GeV(-), and SiV(-) remain photostable up to 180 GPa. We also find that the spin-orbit splitting increases in both the electronic ground and excited states with increasing pressure. The optical transitions associated with the hyperfine fine structure of the dopant atoms are interpreted using our theoretical framework, which reproduces existing experimental data at zero strain. We show that the hyperfine levels are weakly dependent on magnetic field, and increasing pressure leads to optical transitions at longer wavelengths. Finally, we estimate the spin coherence times of the G4V centers under increasing hydrostatic pressure across different temperature regimes.

Figures (8)

• Figure 1: Schematic diagrams illustrating the fundamental properties of G4V($-$) color centers in diamond. (a) Geometry of the defect. Dashed spheres represent the two vacancies, and the interstitial dopant atom (silicon, germanium, tin, or lead) is shown as a red sphere. The critical distances under high $D_{3d}$ symmetry are labeled as $d_1$ and $d_2$. The dopant atom is positioned at the inversion center of the diamond. (b) Schematic single-particle defect levels in the electronic ground state (small spin-polarization splittings of $\lesssim20$ meV omitted). The positions of the fully occupied double degenerate $e_u$ levels and the partially occupied $e_g$ levels vary in the various G4V($-$) color centers. In the electronic excited state (not shown), the $e_g$ levels are fully occupied, whereas a hole is left on the $e_u$ level. (c) Electronic structure in the ground and excited states, including fine and hyperfine interactions. The hyperfine structure originates from the coupling with the impurity atom positioned at the inversion symmetry point. The fine and hyperfine states are labeled according to the double-group representations of the $D_{3d}$ point group, following the notation in Ref. altmann1994. $\lambda_{g,u}$ are the effective spin-orbit splitting in the $g$ (even parity) ground and $u$ (odd parity) excited states. Transitions between two Kramers states occur with orbital relaxation at rates $\gamma_{\pm}$. The hyperfine coupling parameters $A_{\parallel,\{g,u\}}$ and $A_{2,\{g,u\}}$ lift the degeneracy of the fine-structure states, while $A_{\perp,\{g,u\}}$ and $A_{1,\{g,u\}}$ facilitate the mixing of spin-orbit states. (d) Adiabatic potential energy surface (APES) of the quadratic Jahn-Teller system along the ionic degrees of freedom corresponding to a single degenerate $e_g$-symmetry mode, described by the configuration coordinates $Q_{x,y}$. The points of BS, HS, and S represent the lowest energy broken-symmetry, the highest energy of highest symmetry and saddle point configurations, respectively. $E_\text{JT}$ is the difference in energy between the high symmetry configuration and the distorted configuration. The three equivalent global minima are separated by energy barriers of $\delta_\text{JT}$.
• Figure 2: (a) Calculated charge transition levels of SiV, GeV, SnV and PbV defects under hydrostatic pressure in the range of $0$ to $180$ GPa as obtained by HSE06 functional. (b) The ZPL shift under hydrostatic pressure was calculated by SCAN functional where the zero pressure value was aligned to the experimental data. Calculated ZPL curves have been rigidly shifted to their experimental zero-pressure values (1.68 eV for SiV, 2.06 eV for GeV, and 2.00 eV for SnV). The slight deviation of the GeV data below 20 GPa is due to a pressure-calibration bias during diamond anvil cell loading (see Ref. Vindolet2022). For SiV and GeV defects the experimental data points for non-zero pressure are also given from Ref. Vindolet2022. We highlight the hydrostatic pressure region by light red color where PbV($-$) is not photostable. We list the charge correction to the total energy and dielectric constant dependency on pressure in Table \ref{['table:eps']}.
• Figure 3: Pressure dependent spin-orbit splitting as obtained with SCAN functional where the spin-orbit interaction added as perturbation to the Jahn--Teller-effect. (a) The calculated hydrostatic pressure (GPa) dependence of the effective spin-orbit splitting $\lambda$ in GHz unit for G4V($-$) color centers in the electronic excited and ground states plotted by blue and red lines, respectively. (b) The sum of the electronic excited and ground state's $\lambda$ values associated with the zero-phonon line broadening at elevated measurement temperatures with off-resonant excitation for each G4V($-$) color center as a function of the applied hydrostatic pressure.
• Figure 4: The electron spin density of the SiV($-$) center with low $C_{2h}$ symmetry in the electronic (a) ground and (b) excited states depicted with the isosurface value of $5\times 10^{-3}$$e/$Å.
• Figure 5: Absolute value of the Fermi-contact hyperfine constants in G4V($-$) centers as obtained with HSE06 functional as a function of hydrostatic pressure for (a) dopant atoms and (d) first neighbor carbon atoms. These calculations were carried out in $D_{3d}$ symmetry configurations. The illustration of A$_\text{PLE}$, $A_{\|}^\text{gs}$ and $A_{\|}^\text{exc}$ as a function of hydrostatic pressure for dopant atoms---depicted in green, red and blue colors, respectively---(see text for details) with low $C_{2h}$ point group symmetry for given defect centers of (b) SiV($-$), (c) GeV($-$) , (e) SnV($-$) and (f) PbV($-$). The plots were fit to quadratic functions.