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

TL;DR

This paper investigates vibronic interactions and the Jahn-Teller effect in CuInP$_2$S$_6$ crystals, combining group theory and ab initio calculations to understand phase transitions and potential spontaneous polarization.

Contribution

It introduces a novel approach linking elementary energy bands with vibronic potential energy matrices in crystals, applied to CuInP$_2$S$_6$ to analyze phase transitions.

Findings

Identified the role of copper $d$-electron states in the energy gap.

Constructed adiabatic potentials for vibronic coupling.

Discussed conditions for spontaneous polarization.

Abstract

The order-disorder type phase transition caused by the vibronic interaction (collective Jahn-Teller effect) in a monoclinic CuInP$_2$S$_6$ crystal is analyzed. For this purpose, a trigonal protostructure model of CuInP$_2$S$_6$ is created, through a slight change in the crystal lattice parameters of the CuInP$_2$S$_6$ paraelectric phase. In parallel to the group-theoretical analysis, the DFT-based {\it ab initio} band structure calculations of the CuInP$_2$S$_6$ 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 CuInP$_2$S$_6$ 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.