calculations of temperature dependent electronic structures of inorganic halide perovskite materials.

Despite wide interest in halide perovskite materials, it is still challenging to accurately calculate their electronic structure and its temperature dependence. In this work, we present calculations of the temperature dependence of the electronic structure of CsPbX materials (X = Cl, Br or I) in the cubic form and of the zero temperature electronic structure of the orthorhombic phase of these materials. Phonon-induced temperature dependent band energy renormalization was calculated within the framework of Allen-Heine-Cardona theory, where we exploited the self-consistent procedure to determine both the energy level shifts and their broadenings. The phonon spectrum of the materials was obtained using the self-consistent phonon method since standard density functional perturbation theory calculations in harmonic approximation yield phonon modes with imaginary frequencies due to the fact that the cubic structure is not stable at zero temperature. Our results suggest that low energy phonon modes mostly contribute to phonon-induced band energy renormalization. The calculated values of the band gaps at lowest temperature where the material exhibits a cubic structure are in good agreement with experimental results from the literature. The same is the case for the slope of the temperature dependence of the band gap for the CsPbI material where reliable experimental data are available in the literature. We also found that phonon-induced temperature dependence of the band gap is most pronounced for the conduction band minimum and valence band maximum, while other bands exhibit a weaker dependence.