Halide perovskites are strongly influenced by large amplitude anharmonic lattice fluctuations at room temperature. We develop a tight-binding model for dynamically disordered ${\mathrm{MAPbI}}_3$ based on density functional theory calculations to calculate electronic structure for finite temperature crystal structures at the length scale of thermal disorder and carrier localization. The model predicts individual Hamiltonian matrix elements and band structures with high accuracy, owing to the inclusion of additional matrix elements and descriptors for non-Coulombic interactions. We apply this model to electronic structure at length and timescales inaccessible to first-principles methods, finding an increase in band gap, carrier mass, and the subpicosecond fluctuations in these quantities with increasing temperature as well as the onset of carrier localization in large supercells induced by thermal disorder at 300 K. We identify the length scale $L^{*}=5$ nm as the onset of localization in the electronic structure, associated with decreasing band edge fluctuations, increasing carrier mass, and Rashba splitting approaching zero.

• Received 13 May 2021
• Revised 19 July 2021
• Accepted 3 August 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.085404