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We report a model study of the phonon response on the interplay of thesuperconducting (SC) gap and both static and dynamic Jahn-Teller distortion andpredict the appearance of the SC and Jahn-Teller (JT) distortion gap excitationpeaks in the Raman spectra of high-Tc superconductors. The model consists ofthe Hamiltonian containing static JT interaction and s-wave type SC interactionin the conduction band. Further the phonons are coupled to the density of theconduction electron in the band as well as to the JT split conduction bandgiving rise to dynamic Jahn-Teller (DJT) interaction. The phonons areconsidered in a harmonic approximation. The phonon Green's function iscalculated by Zubarev's technique and the phonon self-energy arising due tonormal electron-phonon (EP) interaction and DJT interaction. The phononself-energy arising due to this is calculated from the electron responsedensity function in the coexistence phase of the two order parameters. Thephonon spectral density predicts two excitation peaks, one due to SC gap andthe other due to JT distortion. The DJT coupling suppresses the JT gap while itenhances SC gap as well as SC transition temperature. The evolution of theseexcitation peaks are investigated by varying different model parameters of thesystem.

Dynamic Jahn-Teller effect and superconducting excitations in Raman spectra