Small hole polarons in yellow phase $\delta$-CsPbI${}_3$

A heterophase containing both the optically active $\alpha$-CsPbI${}_3$ and non-active $\delta$-CsPbI${}_3$ has been demonstrated as an efficient white light emitter. This has challenged the conventional perspective that non-active phases of perovskites are undesirable in any perovskite-based optoelectronic devices. To understand the role that the yellow phase $\delta$-CsPbI${}_3$ plays in the light emission process, we performed a systematic computational study on its electronic and optical properties, which are relatively unexplored in the literature. Using the Fröhlich model we showed that the electron and hole both exhibit moderate coupling to longitudinal optical phonons. Explicit density functional theory calculations show that small hole polarons exist with a formation energy of -96 meV, corresponding to the contraction of the Pb-I bonds within a [PbI${}_6$] octahedra and wavefunction localization. Molecular dynamics simulations showed that the small hole polaron is stable against thermal disorder, and exhibit periodic localization and delocalization behavior similar to carrier hopping with a characteristic lifetime of 0.3 ps. Our results might have elucidated the role that $\delta$-CsPbI${}_3$ play in the self-trapped emission in perovskite-based white light emitting diodes by supporting the presence of a localized small hole polaron.