Wave Function\nLocalization Reduces the Bandgap of\nDisordered Double Perovskite Cs<sub>2</sub>AgBiBr<sub>6</sub>

Double perovskite Cs<sub>2</sub>AgBiBr<sub>6</sub> is\na promising\nalternative to lead-based perovskites with excellent stability and\nattractive optoelectronic properties. However, a relatively large\nbandgap severely limits its performance in many applications such\nas solar cells and photodetectors. It has been reported that a random\ndistribution of Ag and Bi atoms in Cs<sub>2</sub>AgBiBr<sub>6</sub> effectively reduces its bandgap without introducing dopants or impurities,\nwhile the mechanism remains unclear. Here, using density functional\ntheory calculations, we demonstrate that the Ag–Bi disorder\nin Cs<sub>2</sub>AgBiBr<sub>6</sub> generates localized electronic\nstates as band edges to regulate the bandgap. The disordered structures\nsegregate Ag and Bi atoms in the lattice, and the formed homoatomic\nclusters lead to wave function localization. Moreover, the bandgap\ndecrease exhibits a non-monotonic dependence on the degree of disorder.\nOur results are comparable with experimental observations and provide\ncrucial insights into understanding the order–disorder transition\nin double perovskites.