All-electron $\mathrm{\textit{ab-initio}}$ hyperfine coupling of Si-, Ge- and Sn-vacancy defects in diamond

TL;DR

This paper presents the first all-electron extit{ab-initio} calculations of hyperfine couplings for SiV, GeV, and SnV defects in diamond, providing key data for quantum applications and guiding future experiments.

Contribution

It introduces novel all-electron extit{ab-initio} hyperfine coupling calculations for SiV, GeV, and SnV defects in diamond, including the defect atoms and surrounding carbon isotopes.

Findings

Hyperfine couplings depend linearly on the Hartree-Fock mixing parameter.

Predicted hyperfine constants are close to existing experimental values.

Calculated nuclear quadrupole moments for GeV defect.

Abstract

Colour centres in diamond are attractive candidates for numerous quantum applications due to their good optical properties and long spin coherence times. They also provide access to the even longer coherence of hyperfine coupled nuclear spins in their environment. While the NV centre is well studied, both in experiment and theory, the hyperfine couplings in the more novel centres (SiV, GeV, and SnV) are still largely unknown. Here we report on the first all-electron \textit{ab-initio} calculations of the hyperfine constants for SiV, GeV, and SnV defects in diamond, both for the respective defect atoms ($^{29}$Si, $^{73}$Ge, $^{117}$Sn, $^{119}$Sn), as well as for the surrounding $^{13}$C atoms. Furthermore, we calculate the nuclear quadrupole moments of the GeV defect. We vary the Hartree-Fock mixing parameter for Perdew-Burke-Ernzerhof (PBE) exchange correlation functional and show that the hyperfine couplings of the defect atoms have a linear dependence on the mixing percentage. We calculate the inverse dielectric constant to predict an \textit{ab-initio} mixing percentage. The final hyperfine coupling predictions are close to the experimental values available in the literature. Our results will help to guide future novel experiments on these defects.