First-principles predictions of qubits in defective MgS

In this paper, MgS is evaluated to be a suitable qubit host material due to its wide bandgap, being nuclear spin free, and its weak spin-orbit coupling. The point defects including vacancies, substitutions, and defect pairs were systematically investigated using first-principles calculations. Results show that the neutral ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}$ defect pair has $C_{3v}$ symmetry with the defect level sequence of $E_1>E_{exy}>E_2$. In addition, the net spin and defect levels of ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}$ can be tuned by charge states. The ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}^{2+}$ and ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}^{2-}$ defects are relatively stable with the charge transition level of ∼2.53 eV. The four charged defect states of ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}^{+}$, ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}^{2+}$, ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}^{-}$, and ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}^{2-}$ may be plausible qubits with nonzero spin, and their zero-phonon lines indicate the corresponding fluorescence wavelengths fall within the infrared band. Furthermore, the zero field splitting of the ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}^{+}$ and ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}^{-}$ shows that the values of parameter $D$ are in the range of microwaves. The hyperfine constants are roughly proportional to the spin difference charge density and exponentially decay as a function of the distance from the P site.

Figure 1

(a) Structure, (b) electronic properties, (c) phonon spectrum, and (d) band structures of MgS without and with spin-orbit coupling (SOC) of MgS primitive. The electronic properties were calculated at the HSE06 level and the SOC calculated at the PBE level.

Figure 2

Schematic diagram of each point defect configuration in a 2 × 2 × 2 MgS supercell.

Figure 3

(a) Configuration of the ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}$ defect in MgS, (b) the corresponding projected density of states (PDOS), (c) the band structure, and (d) the amplified band structure with an energy range of −1.0 to 1.0 eV. The two channels of spin-up and spin-down states are marked by blue and red lines, respectively.

Figure 4

The schematic diagram of defect energy levels sequence. The red arrow represents the occupied states, and the two channels of spin-up and spin-down states are marked by up and down arrows, respectively.

Figure 5

The partial charge density of molecular orbitals in the ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}$ defect in the order of energy from high to low. The isosurface value is $2\times {10}^{-3}\mathrm{e}/{\AA }^3$. The two channels of spin-up and spin-down states are marked by up and down arrows, respectively.

Figure 6

The calculated defect formation energy of the ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}$ defect center in different charge states as a function of Fermi levels.

Figure 7

The schematic diagram of the defect levels in the ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}$ center in different charge states. $q$ and $S$ represent the charge state and net spin, respectively. The red arrow represents the occupied states, and the green arrow represents the electron transition. The two channels of spin-up and spin-down states are marked by up and down arrows, respectively.

Figure 8

The configuration coordinate diagram. $E$ and $q$ represent the total energy and the configuration coordinate, respectively. The blue and green arrows represent vertical absorption and vertical emission, respectively, and the red arrow is the zero-phonon line (ZPL). $\mathrm{\Delta }S$ and $\mathrm{\Delta }AS$ stand for Stokes shift and anti-Stokes shift, respectively.

Figure 9

Schematic diagram about energy levels of the ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}^{2-}$ defect.

Figure 10

Schematic diagram of (a) the local structure and (b) and (c) the spin difference charge density of the ${\mathrm{P}}_{\mathrm{S}}{\mathrm{V}}_{\mathrm{Mg}}$ defect pair in MgS. We only show the atoms up to the second neighbors from the nucleus site; the isosurface value is $1\times {10}^{-3}\mathrm{e}/{\AA }^3$ for the spin difference charge density.