Effective model for studying optical properties of lead-halide perovskites

We use general symmetry-based arguments to construct an effective model suitable for studying optical properties of lead-halide perovskites. To build the model, we identify an atomic-level interaction between electromagnetic fields and the spin degree of freedom that should be added to a minimally-coupled $\mathbf{k\cdot p}$ Hamiltonian. As a first application, we study two basic optical characteristics of the material: the Verdet constant and the refractive index. Beyond these linear characteristics of the material the model is suitable for calculating non-linear effects such as the third-order optical susceptibility. Analysis of this quantity shows that the geometrical properties of the spin-electric term imply isotropic optical response of the system, and that optical anisotropy of lead-halide perovskites is a manifestation of hopping of charge carriers. To illustrate this, we discuss third-harmonic generation.