Equal Footing of Thermal Expansion and Electron-Phonon Interaction in the Temperature Dependence of Lead Halide Perovskite Band Gaps

Lead halide perovskites, which are causing a paradigm shift in photovoltaics, exhibit an atypical temperature dependence of the fundamental gap: it decreases in energy with decreasing temperature. Reports ascribe such a behavior to a strong electron-phonon renormalization of the gap, neglecting contributions from thermal expansion. However, high-pressure experiments performed on the archetypal perovskite MAPbI(3) (MA stands for methylammonium) yield a negative pressure coefficient for the gap of the tetragonal room-temperature phase, which speaks against the assumption of negligible thermal expansion effects. Here we show that for MAPbI(3) the temperature-induced gap renormalization due to electron-phonon interaction can only account for about 40% of the total energy shift, thus implying thermal expansion to be more if not as important as electron- phonon coupling. Furthermore, this result possesses general validity, holding also for the tetragonal or cubic phase, stable at ambient conditions, of most halide perovskite counterparts.