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

In recent years, the negatively charged group-IV--vacancy defects in diamond, labeled as $\mathrm{G}4\mathrm{V}(\ensuremath{-}$) 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 $\mathrm{SiV}(\ensuremath{-}$) to $\mathrm{PbV}(\ensuremath{-}$). On the other hand, our calculated photoionization threshold energies indicate that $\mathrm{PbV}(\ensuremath{-}$)-based quantum sensors can operate only up to 32 GPa, whereas $\mathrm{SnV}(\ensuremath{-}$), $\mathrm{GeV}(\ensuremath{-}$), and $\mathrm{SiV}(\ensuremath{-}$) 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.