PHONON RENORMALIZATION AND SYMMETRY OF THE SUPERCONDUCTING ORDER-PARAMETER

We present a method for the calculation of the renormalization of the phonon energy in the superconducting state. The expression is derived in the weak-coupling case and takes into account the k dependency of the order parameter Delta(k). The phonon shift as well as the linewidth are calculated. The influence of the anisotropy of the gap in the ab plane of the high-T-c superconductors on the renormalization of the q-->O phonon energies is studied. The anisotropies considered have either s-, d-wave, or mixed character. It is shown that an anisotropic gap with s-wave symmetry leads to a renormalization of the phonon energy below T-c that is in agreement with the Raman measurements. The renormalization resulting from the d-wave case instead is incompatible with these experiments. Finally, the strength of the electron-phonon coupling is estimated for the Raman observed phonons.