Lattice dynamics in perovskite halidesCsSnX3withX=I, Br, Cl

The first-principles linear response method is used within the local-density approximation to calculate the full phonon band structures and phonon density of states (DOS) of $\mathrm{CsSn}{X}_{3}$ ($X=\text{Cl}$, Br, or I) in different phases. The relations between soft phonon modes and phase transitions are investigated. We find soft phonon modes only in the cubic and tetragonal phases, not in the orthorhombic and monoclinic phases. A dispersionless soft phonon branch spreads from the k point $M$ to $R$ in the Brillouin zone of the cubic phase. The lower symmetry tetragonal phase results from the condensation of the soft phonon mode at the k point $M$. Furthermore, the condensation of the soft phonon mode at the k point $Z$ in the Brillouin zone of tetragonal phase results in the orthorhombic $\ensuremath{\gamma}$ phase. To facilitate comparison with experimental data, we calculate infrared spectra for the cubic phase. At this point only a limited comparison with experimental data is possible. We find that the calculated modes agree with the available experimental data when we assign the second and third calculated modes to the experimental first and second modes. The lowest calculated mode is at a frequency where the phonon DOS has a maximum value. So the strong phonon-phonon interaction results in short phonon lifetime or strong broadening, which could explain why this mode has not been observed. Our first-principles calculated IR spectra show that the third observed mode in IR absorption is actually the highest longitudinal optical (LO) rather than transverse optical mode. We show, furthermore, that a strong LO-plasmon coupling may be expected in these materials and can explain observed Raman data for ${\mathrm{CsSnI}}_{3}$.