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.