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

TL;DR

This paper uses a self-consistent t-matrix approximation to interpret microwave conductivity measurements in YBCO superconductors, revealing insights into impurity scattering mechanisms at low temperatures.

Contribution

It introduces a method to extract effective self-energy from microwave data, providing new understanding of impurity scattering in d-wave superconductors.

Findings

Effective self-energy approximated by a constant plus linear term in frequency

Impurity scattering phase shift varies from weak to unitary limit

Microwave data reveals small positive slope in self-energy at low energies

Abstract

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.