Electronic Origin of Non-Zone-Center Phonon Condensations: Octahedral Rotations as A Case Study

Unstable zone-boundary phonon modes drive atomic displacements linked to a rich array of properties. Yet, the electronic origin of the instability remains to be clearly explained. Here, we propose that bonding interaction between Bloch states belonging to different wavevectors leads to such instability via the pseudo- or second-order Jahn--Teller effect. Our first-principles calculations and representation theory-based analyses show that rotations of anion coordinated octahedra, an archetypal example of zone-boundary phonon condensations, are induced by this bonding mechanism. The proposed mechanism is universal to any non-zone-center phonon condensations and could offer a general approach to understand the origin of structural phase transitions in crystals.