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We determine the impact of anharmonic thermal vibrations on the fundamentalband gap of CsPbBr$_3$, a prototypical model system for the broader class ofhalide perovskite semiconductors. Through first-principles molecular dynamicsand stochastic calculations, we find that anharmonic fluctuations are a keyeffect in the electronic structure of these materials. We present experimentaland theoretical evidence that important characteristics, such as a mildlychanging band-gap value across a temperature range that includesphase-transitions, cannot be explained by harmonic phonons thermally perturbingan average crystal structure and symmetry. Instead, the thermal characteristicsof the electronic structure are microscopically connected to anharmonicvibrational contributions to the band gap that reach a fairly large magnitudeof 450 meV at 425 K.

Anharmonic Fluctuations Govern the Band Gap of Halide Perovskites