Methods to Accelerate High-Throughput Screening of Atomic Qubit Candidates in van der Waals Materials

The discovery of atom-like spin emitters associated with defects in two-dimensional (2D) wide-bandgap (WBG) semiconductors presents new opportunities for highly tunable and versatile qubits. So far, the study of such spin emitters has focused on defects in hexagonal boron nitride (hBN). However, hBN necessarily contains a high density of nuclear spins, which are expected to create a strong incoherent spin-bath that leads to poor coherence properties of spins hosted in the material. Therefore, identification of new qubit candidates in other 2DWBG materials is necessary. Given time demands of $ab~initio$ methods, new approaches for rapid screening and calculation of identifying properties of suitable atom-like qubits are required. In this work, we present two new methods for rapid estimation of the zero-phonon line (ZPL), a key property of atomic qubits in WBG materials. First, this ZPL is calculated by exploiting Janak's theorem. For finite changes in occupation, we provide the leading-order estimate of the correction to the ZPL obtained using Janak's theorem, which is more rapid than the standard method ($\Delta$SCF). Next, we also demonstrate an approach to converging excited states that is faster for systems with small strain than the standard approach used in the $\Delta$SCF method. We illustrate these methods using the case of the singly negatively charged calcium vacancy in SiS$_2$, which we are the first to propose as a qubit candidate. This work has the potential to assist in accelerating the high-throughput search for quantum defects in materials, with applications in quantum sensing and quantum computing.