Phonon Mode Transformation across the Orthohombic-Tetragonal Phase Transition in a Lead-Iodide Perovskite CH$_{3}$NH$_{3}$PbI$_{3}$: a Terahertz Time-Domain Spectroscopy Approach*

Using terahertz time-domain spectroscopy (THz-TDS), we study the temperature-dependent phonon modes of the organometallic lead iodide perovskite CH$_{3}$NH$_{3}$PbI$_{3}$ thin film across the terahertz (0.5-3 THz) and temperature (20-300 K) ranges. These modes are related to the vibration of the Pb-I bonds. We found that two phonon modes in the tetragonal phase at room temperature split into four modes in the low-temperature orthorhombic phase. By use of the Lorentz model fitting, we analyze the critical behavior of this phase transition.