PHONON-RAMAN SCATTERING IN A CORRELATED SUPERCONDUCTOR

The phonon spectral density function is calculated to explain the observed anomalies in the Raman spectrum of the cuprate superconductors. These being strongly correlated systems, their ground state is taken to be the resonating valence bond (RVB) state. In this state, the phonons are shown to couple predominantly to the RVB pair excitations besides the usual interaction with the charge carrier density. It is proposed that the superconductivity in the system appears due to the correlation bag mechanism where the collective excitations of the RVB state mediate an attractive interaction between the charge carriers which leads to pairing. The dependence of the transition temperature on the RVB pp parameter as well as the dopant concentration is demonstrated. The phonon self-energies, which involve the pair correlation function and the density response function, are evaluated at zero temperature for the normal state as well as the superconducting states. It is shown that the pair correlation function strongly renormalises the phonon spectrum. Its spectral density shows a broad peak corresponding to the RVB-amplitude mode, which qualitatively resembles the observed Raman spectrum in the superconducting state.