QUASI-PARTICLE LIFETIMES AND SIGNATURES OF THE SUPERCONDUCTOR ORDER-PARAMETER SYMMETRY IN PHONON LINEWIDTHS

The effect of quasiparticle scattering on the temperature and frequenc y dependences of the imaginary part of the electronic polarizability, ImP((q) over right arrow,omega), is investigated for a d(x)2(-y)2 supe rconducting state with an underlying tight-binding band structure. The work is motivated by a proposal that the lifetime of phonons in the s uperconducting state can provide information on the symmetry of the or der parameter in the cuprate oxide superconductors. In this proposal t he signatures of superconductor order parameter symmetries appear in t he momentum, frequency, and temperature dependence of the phonon self- energy coming from ImP((q) over right arrow omega,w). We use a phenome nological model for the quasiparticle scattering rate which has contri butions from nonmagnetic disorder, interactions among quasiparticles i n the superconducting start, and the (T/T-c)(3) below T-c. We fmd thar modest quasiparticle damping smears our features at frequencies less than or equal to 2 Delta(0) at low temperatures which differentiate be tween different superconducting order-parameter symmetries. Delta(0) i s the maximum magnitude of the gap function Delta(p)(.) at zero temper ature. However, features at higher frequencies arising from the electr onic band structure survive in ImP((q) over right arrow,omega) in the presence of significantly greater quasiparticle damping and provide in formation on the location of low-energy quasiparticle states in the su perconducting phase. These features are also sensitive to finite tempe ratures. The different temperature dependences of ImP((q) over right a rrow,omega) for the s- and d-wave cases at T-T-c are eliminated by bot h quasiparticle damping and the rapid temperature dependence of the su perconducting gap for which there is evidence in the cuprates.