Tight-binding analysis of charge carriers mobilities in MAPbI3 : Strong Fr\"ohlich scattering and quantum localization effects.

We analyze the electronic transport properties of MAPbI3 in a tight-binding model that takes into account the intrinsic thermal disorder at room temperature and also additional extrinsic disorder. A fully quantum transport calculation shows that electrons and holes are strongly scattered by the Frohlich interaction with longitudinal optical phonon modes. This limits the mobilities at room temperature to the order of 200 cm$^2$/Vs . We show that quantum localization effects are important even for these values of the mobility and increase with additional extrinsic disorder. For mobilities below $\mu_{c} \simeq 50 cm^2/Vs$ we find that a large fraction of the states close to band edges are localized and would be insulating if the lattice were static. Yet these electronic states diffuse because they adapt nearly adiabatically to the change of the electrostatic potential due to the dynamics of the lattice. This process of electronic diffusion, driven by the lattice dynamics, should contribute to the unique electronic properties of this material.