Hybrid organic-inorganic perovskites emerged as a new generation of absorber materials for high-efficiency low-cost solar cells in 2009. Very recently, fully inorganic perovskite quantum dots also led to promising efficiencies, making them a potentially stable and efficient alternative to their hybrid cousins. Currently, the record efficiency is obtained with CsPbI, whose crystallographical characterization is still limited. Here, we show through high-resolution in situ synchrotron XRD measurements that CsPbI can be undercooled below its transition temperature and temporarily maintained in its perovskite structure down to room temperature, stabilizing a metastable perovskite polytype (black γ-phase) crucial for photovoltaic applications. Our analysis of the structural phase transitions reveals a highly anisotropic evolution of the individual lattice parameters versus temperature. Structural, vibrational, and electronic properties of all the experimentally observed black phases are further inspected based on several theoretical approaches. Whereas the black γ-phase is shown to behave harmonically around equilibrium, for the tetragonal phase, density functional theory reveals the same anharmonic behavior, with a Brillouin zone-centered double-well instability, as for the cubic phase. Using total energy and vibrational entropy calculations, we highlight the competition between all the low-temperature phases of CsPbI (γ, δ, β) and show that avoiding the order-disorder entropy term arising from double-well instabilities is key to preventing the formation of the yellow perovskitoid phase. A symmetry-based tight-binding model, validated by self-consistent GW calculations including spin-orbit coupling, affords further insight into their electronic properties, with evidence of Rashba effect for both cubic and tetragonal phases when using the symmetry-breaking structures obtained through frozen phonon calculations.

On the basis of a general symmetry analysis, this paper presents an empirical tight-binding (TB) model for the reference Pm-3m perovskite cubic phase of halide perovskites of general formula ABX. The TB electronic band diagram, with and without spin orbit coupling effect of MAPbI has been determined based on state of the art density functional theory results including many body corrections (DFT+GW). It affords access to various properties, including distorted structures, at a significantly reduced computational cost. This is illustrated with the calculation of the band-to-band absorption spectrum, the variation of the band gap under volumetric strain, as well as the Rashba effect for a uniaxial symmetry breaking. Compared to DFT approaches, this empirical model will help to tackle larger issues, such as the electronic band structure of large nanostructures, including many-body effects, or heterostructures relevant to perovskite device modeling suited to the description of atomic-scale features.