A structure in a phonon spectral function induced by superconductivity

Abstract

A superconducting gap resonating with a phonon makes a structure in the phonon spectral function even in the d-wave pairing. This is demonstrated by a theoretical calculation. The conditions employed in our calculations are q→0 and the clean limit where q is the momentum of the phonon. The difference in the line shape of the phonon between the s-wave model and d-wave mode is noticeable. The resonance structure would be observed in the Raman spectrum when the phonon propagates in ab-plane, i.e., the directions of the incident light and scattered light are perpendicular to c-axis. We propose a new method to investigate the symmetry of superconducting gap function in the cuprate superconductor through this resonance structure.