Vibronic interaction in crystals with the Jahn-Teller centers in the elementary energy bands concept

The order-disorder type phase transition caused by the vibronic interaction (collective Jahn-Teller effect) in a monoclinic CuInP2S6 crystal is analyzed. For this purpose, a trigonal protostructure model of CuInP2S6 is created, through a slight change in the crystal lattice parameters of the CuInP2S6 paraelectric phase. In parallel to the group-theoretical analysis, the DFT-based ab initio band structure calculations of the CuInP2S6 protostructure, para-, and ferriphases are performed. Using the elementary energy bands concept, a part of the band structure from the vicinity of the forbidden energy gap, which is created by the d-electron states of copper, has been related with a certain Wyckoff position where the Jahn-Teller's centers are localized. A construction procedure of the vibronic potential energy matrix is generalized for the case of crystal using the elementary energy bands concept and the group theoretical method of invariants. The procedure is illustrated by the creation of the adiabatic potentials of the Gamma(5)-Gamma(5) vibronic coupling for the protostructure and paraphase of the CuInP2S6 crystal. A structure of the obtained adiabatic potentials is analyzed, followed by conclusions on their transformation under a phase transition and the discussion on the possibility for the spontaneous polarization to arise in this crystal.