Microwave Conductivity due to Impurity Scattering in a d-wave Superconductor

The self-consistent t-matrix approximation for impurity scattering in unconventional superconductors is used to interpret recent measurements of the temperature and frequency dependence of the microwave conductivity of YBCO crystals below 20K. In this theory, the conductivity is expressed in terms of a fequency dependent single particle self-energy, determined by the impurity scattering phase shift which is small for weak (Born) scattering and approaches $\pi / 2$ for unitary scattering. Inverting this process, microwave conductivity data are used to extract an effective single-particle self-energy and obtain insight into the nature of the operative scattering processes. It is found that the effective self-energy is well approximated by a constant plus a linear term in frequency with a small positive slope for thermal quasiparticle energies below 20K. Possible physical origins of this form of self-energy are discussed.