Stability of the Negatively Charged Calcium Vacancy in Monolayer SiS$_2$ and Exploiting Janak's Theorem for ZPL Calculations

In this work, we provide density-functional theory (DFT) calculations to determine the stability and zero-phonon line (ZPL) of the singly negatively charged calcium vacancy in SiS$_2$. This ZPL is calculated in the hole picture by exploiting Janak's theorem, encouraged by the accuracy of the approach when applied to silicon monovacancies in $4H$-SiC. We provide a lowest order estimate of the error associated with this method, the computation of which is more rapid than the standard $\Delta$SCF calculation. We ultimately propose the new singly negatively charged calcium vacancy in SiS$_2$ as a qubit candidate, which we predict should exhibit inversion symmetry, and suggest that Janak's theorem could be used to screen large numbers of potential point defect qubit candidates for optimal ZPL values.