Microwave Conductivity due to Scattering from Extended Linear Defects in d-Wave Superconductors

Recent microwave conductivity measurements of detwinned, high-purity, slightly overdoped YBa$_{2}$Cu$_{3}$O$_{6.993}$ crystals reveal a linear temperature dependence and a near-Drude lineshape for temperatures between 1 and 20 K and frequencies ranging from 1 to 75 GHz. Prior theoretical work has shown that simple models of scattering by point defects (impurities) in d-wave superconductors are inconsistent with these results. It has therefore been suggested that scattering by extended defects such as twin boundary remnants, left over from the detwinning process, may also be important. We calculate the self-energy and microwave conductivity in the self-consistent Born approximation (including vertex corrections) for a d-wave superconductor in the presence of scattering from extended linear defects. We find that in the experimentally relevant limit ($\Omega, 1/\tau \ll T \ll \Delta_{0}$), the resulting microwave conductivity has a linear temperature dependence and a near-Drude frequency dependence that agrees well with experiment.