First-principles calculations of electron-phonon interactions with GW corrections for localized defect states in monolayer WS₂ with a sulfur vacancy

Recent scanning tunneling spectroscopy measurements on a sulfur vacancy (V_S) in monolayer WS₂ have observed that in-gap defect states feature prominent sideband structure, a signature of strong electron-phonon (el-ph) interactions. Here, we use a combination of density functional theory (DFT) and ab initio many-body perturbation theory within the GW approximation to calculate defect states associated with V_S in monolayer WS₂ and their el-ph interactions. For each vibrational state, we compute Huang-Rhys factors via first-principles including spin-orbit coupling (SOC) in a fully relativistic way. We find that just a few specific phonon modes couple strongly with the defect levels and that two defect levels split by SOC couple to the same modes, but different strengths. We also find that inclusion of exact exchange and electron-electron correlations using the GW method substantially renormalizes the coupling strength in a mode-dependent fashion, giving rise to better agreement with experimental spectral lineshapes. This work enables a deeper understanding of el-ph interactions in systems that feature localized electronic states and provides a route for predicting spectral features associated with defects with higher accuracy using first-principles calculations.