Group-theoretical analysis of crystal and phonon structures of pseudocubic, tetragonal, and orthorhombic methylammonium lead iodide

The phonons of methylammonium lead iodide (CH₃NH₃PbI₃), a prototypical organic-inorganic hybrid perovskite material, have long been measured and calculated, yet the connection between the orthorhombic/tetragonal phases and the soft phonons in the pseudocubic phase has not been clearly identified. Here a true pseudocubic structure, fully respecting the C_3v point group of the organic cation and retaining the cubic inorganic cage, is proposed as a representative initial state for condensing soft phonons. We perform phonon calculations on the pseudocubic, tetragonal, and orthorhombic phases of CH₃NH₃PbI₃ using the irreducible derivative approach and analyze the structural phase transitions in terms of the condensation of soft phonon modes. A group-theoretical analysis of the phonon interactions reveals the connection between the low symmetry crystal structures and the soft modes of the pseudocubic phase, where the tetragonal structure is dominated by R-point soft modes and the orthorhombic phase by an M-point soft mode. Moreover, based on the phonon structures of the low-symmetry phases, we compute the tetragonal-orthorhombic phase transition of CH₃NH₃PbI₃ within the harmonic approximation.