Quasiparticle and Phonon Lifetimes in the Layered Cuprate Superconductors.

In this dissertation we examine quasiparticle and phonon lifetimes in the layered copper-oxide superconductors. We calculate the quasiparticle lifetime arising from spin -fluctuation scattering as well as that due to impurity scattering within a weak coupling model of superconductivity in these materials. We first consider the effects of these lifetimes on the low frequency conductivity and compare to recent experiments. For temperatures above about T _{c}/2, we find that the experimental results are consistent with the d-wave results for a quasiparticle lifetime driven by spin-fluctuation scattering. At lower temperatures, where impurity scattering should dominate, we find that the impurity scattering quasiparticle lifetime has too much frequency structure to be consistent with current microwave surface resistance measurements. We also consider the effects of quasiparticle lifetimes on the momentum structure of the spin susceptibility. We find that impurity scattering effects act to restore the zone edge peaks in the imaginary part of the spin susceptibility, which are otherwise suppressed by a d-wave superconducting gap. At the highest impurity concentration considered here, the predicted amount of suppression of the imaginary part of the spin susceptibility in the superconducting state compared to the normal state is in qualitative agreement with the experimental results in that the predicted neutron scattering intensity at the zone edge and along the diagonal is suppressed by about one half in the superconducting state compared to the normal state. The peak structure predicted by this model, however, differs from the experimental results in that the peaks narrow appreciably at low temperatures compared to the normal state. Finally, we examine the influence of superconducting order parameter symmetry on phonon lifetimes due to electron -phonon scattering. We find that changes in phonon lifetimes as a function of temperature and frequency are strongly dependent on both the magnitude and phase of the superconducting order parameter. This allows us to propose a method for mapping the magnitude and phase of the order parameter at different points on the Fermi surface by measuring these lifetimes.