STRONG NONADIABATIC INTERACTIONS AND PHASE-TRANSITIONS IN CONDUCTIVE JAHN-TELLER CRYSTALS

A model of a conducting crystal composed of quasi-molecules with D4h symmetry and with nearly degenerate A1g and B1g states is considered. The model Hamiltonian includes intramolecular strong non-adiabatic interactions, which are non-diagonal with respect to the electronic quantum numbers and linear (Jahn-Teller type) and quadratic (Renner-type) in the vibrational coordinates. The model Hamiltonian is analysed with the help of the mean field method. It is shown that the non-adiabatic electron phonon interaction, causes a structural phase transition which splits the degenerate vibrational mode involved in the interaction, the minimum frequency of the lower branch decreasing when the temperature decreases. For the electrons the two-band BCS equation follows from the calculation, the interaction constant being multiplied by the average number of low-frequency phonons.