Electron-Phonon Interaction as a Mechanism of Phase Transition in the $CuInP_{2}S_{6}$ Crystal

Studies on the phases of $CuInP_{2}S_{6}$ crystal exhibiting phase transitions of the order-disorder type are performed. A possibility for the cooperative Jahn-Teller effect to occur in this crystal is analyzed. For this purpose, the procedure of constructing the potential energy matrix is generalized for the case of crystal and it is illustrated by the construction of the adiabatic potentials for $Γ_{5}$-$Γ_{5}$ vibronic coupling for the proto- and paraelectric phases of $CuInP_{2}S_{6}$. The structure of the obtained potentials is analyzed together with the discussion on the appearance of spontaneous polarization in this crystal.