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Effect of finite quasiparticle lifetime on the frequency dependence of phonon lifetimes in d{sub x{sup 2}{minus}y{sup 2}} superconductors

The frequency dependence of phonon lifetimes in a superconductor with a d{sub x{sup 2}{minus}y{sup 2}} order parameter is investigated. The authors show that the inclusion of a finite quasiparticle lifetime due to impurity scattering and spontaneous quasiparticle decay smears features, recently proposed as signatures of d-wave superconductivity in cuprate superconductors. They show also that the tight-binding bandstructure leads to features at high frequencies associated with superconductivity. These features may serve as a new probe of the shape of the Fermi surface in cuprate superconductors.