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Capturing Excitonic Effects in Lead Iodide Perovskites from Many-Body Perturbation Theory

Lead iodide perovskites have attracted considerable interest in the upcoming photovoltaic technologies and optoelectronic devices. Therefore, an accurate theoretical description of the electronic and optical properties especially to understand the excitonic effects in this class of materials is of scientific and practical interest. However, despite several theoretical research endeavours in past, the most accurate analysis of the key electronic parameters for solar cell performance, such as optical properties, effective mass, exciton binding energy (E$_B$) and the radiative exciton lifetime are still largely unknown. Here, we employ state-of-the-art first-principles based methodologies viz. hybrid functional(HSE06) combined with spin-orbit coupling (SOC), many-body perturbation theory (GW, BSE), model-BSE (mBSE), Wannier-Mott (WM) and Density Functional Perturbation Theory (DFPT). By taking a prototypical model system viz. APbI$_3$ (A = Formamidinium (FA), methylammonium (MA), and Cs), an exhaustive analysis is presented on the theoretical understanding of the optical, electronic and excitonic properties. We show that tuning of exact exchange parameter ($α$) in HSE06 calculations incorporating SOC, followed by single shot GW, and BSE play a pivotal role in obtaining a reliable predictions for the experimental bandgap. We demonstrate that mBSE approach improves the feature of optical spectra w.r.t experiments. Furthermore, WM approach and ionic contribution to dielectric screening (below 16 meV) ameliorate the E$_B$. Our results reveal that the direct-indirect band gap transition (Rashba splitting) may be a factor responsible for the reduced charge carrier recombination rate in MAPbI$_3$ and FAPbI$_3$. The role of cation ''A'' for procuring the long-lived exciton lifetime is well understood. This proposed methodology allows to design new materials with tailored excitonic properties.