Infrared optical absorption of Fr$\ddot{o}$hlich polaron in metal halide perovskites


 The formation of Fr$\ddot{o}$hlich polaron in metal halide perovskites, arising from the charge carrier-longitudinal optical (LO) phonon coupling, has been proposed to explain their exceptional properties, but the effective identification of polaron in these materials is still a challenge task. Herein, we theoretically present the infrared optical absorption of Fr$\ddot{o}$hlich polaron based on Huang-Rhys model. We find that multiphonon overtones are appeared as the energy of incident photon matches the multiple LO phonons, wherein the average phonon numbers of a polaron can be directly evaluated by the order of the strongest overtone. These multiphonon structures sensitively depend on the scale of electronic distribution in the ground state and the dimensionality of the perovskite materials, which gives the enlightenment for the effective modulation of competing processes between the polaron formation and carrier cooling. Moreover, the order of the strongest overtone shifts to the higher ones with temperature, providing a potential proof of the carriers mobility affected by LO phonons scattering. The present model not only suggests a direct way to verify Fr$\ddot{o}$hlich polaron, but also enriches the understanding of the polaron properties in metal halide perovskites.