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Strong Non‐Adiabatic Interactions and Phase Transitions in Conductive Jahn‐Teller Crystals
Author(s) -
Kiselev A. A.,
Liaptsev A. V.
Publication year - 1992
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221690225
Subject(s) - degenerate energy levels , hamiltonian (control theory) , jahn–teller effect , adiabatic process , phonon , condensed matter physics , physics , adiabatic theorem , diagonal , quantum mechanics , electron , ion , mathematics , geometry , mathematical optimization
A model of a conducting crystal composed of quasi‐molecules with D 4h symmetry and with nearly degenerate A 1g and B 1g 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.