Accelerating GW calculations of point defects with the defect-patched screening approximation

GW method is considered as an established ab initio tool for calculating defect levels. However, the GW simulation cost increases dramatically with the system size, and, unfortunately, large supercells are often required to model low-density defects that are experimentally relevant. In this work, we propose to accelerate GW calculations of point defects by reducing the simulation cost of the many-electron screening, which is the primary computational bottleneck. The random-phase approximation of many-electron screening is divided into two parts: one is the intrinsic screening, calculated using a unit cell of pristine structures, and the other is the defect-induced screening, calculated using the supercell within a small energy window. Depending on specific defects, one may only need to consider the intrinsic polarizability or include the defect contribution. This approach avoids the summation of many conductions states of supercells and significantly reduces the simulation time. We have applied it to calculating various point defects, including neutral and charged defects in two-dimensional and bulk systems with small or large energy gaps. The results consist with direct GW results, and the agreements are further improved at the dilute-defect limit, which is experimentally relevant but extremely challenging for direct GW simulations. This defect-patched screening approach clarifies the roles of defects in many-electron screening and can fast screen defect structures/materials for novel applications, including single-photon sources, quantum qubits, and quantum sensors.