Dynamical Rashba Band Splitting in Hybrid Perovskites Modeled by Local Electric Fields

We report a computational method for evaluating the dynamical Rashba Interaction Coefficient (RIC) of tetragonal and cubic methylammonium lead iodide (MAPbI3) perovskite, at meso- and microscopic size scales, through Car-Parinello Molecular Dynamics (CPMD) trajectories which was hitherto never reported in the literature. This strategy involves the calculation of a time-dependent band structure of the target systems using periodic boundary conditions, and the evaluation of the amplitude of band-splitting due to the Spin-Orbit Coupling (SOC) with the computation of a local electric field. This model, physically motivated by a rewriting of the SOC Hamiltonian according to the heterogeneity of three-dimensional systems and our choice of k-space sampling, involves directly the methylammonium (MA) configuration space sampling. Originally applied to tetragonal and cubic unit cells with static point-charges, this model is further ameliorated in order to take into account the replication of this unit cell through space, and to account for the dynamical nature of charge distribution. Once our protocol has been calibrated based on a toy model, it is exploited for investigating MAPbI3 systems in both tetragonal and cubic phases.