Pseudo Jahn Teller Effect and Ferroelectric Transitions in Group IV Tellurides

Group IV tellurides exhibit ferroelectric phase transitions depending on the cation. We study the ferroelectric transition of group IV tellurides in the notion of the pseudo Jahn-Teller effect (PJTE). While PJTE describes satisfactorily finite molecular systems, its application to solids is not straightforward due to the lack of formalisms adequate for crystals. We demonstrate how the PJTE can be reiterated in the framework of density functional theory and in terms of Kohn-Sham states. Using the density functional perturbation theory (DFPT), we express the terms of PJTE for solids, which can be interpreted as electron-phonon coupling. Considering the electronic states in specific energy ranges on the electron-phonon interaction, we investigate the phonon softening and ferroelectric transition of the tellurides. We analyze how the electronic structures and their symmetry affect the phonon softening within the framework of PJTE.