Microwave Conductivity of a High Purity d-wave Superconductor

TL;DR

This paper investigates the microwave conductivity in a high purity d-wave superconductor, revealing how impurity scattering and magnetic vortices influence its frequency-dependent behavior at low temperatures.

Contribution

It demonstrates the direct link between microwave conductivity cusp behavior and impurity scattering rate linearity, and predicts a Drude-like response in the vortex state.

Findings

Microwave conductivity exhibits cusp-like behavior at low temperature.

Impurity scattering rate is linear in frequency with a small zero-frequency value.

Magnetic vortices induce a finite zero-frequency impurity scattering rate, leading to a Drude-like conductivity.

Abstract

The cusp-like behavior of the microwave conductivity observed in clean ortho-II YB$_{2}$Cu$_{3}$O$_{6.50}$ at low temperature and low frequency is shown to be related directly to a linear in frequency dependence of the impurity scattering rate with a negligibly small value at zero frequency. In the weak scattering limit, the conductivity decreases linearly with the frequency. In the vortex state, assuming a random (Gaussian) distribution of vortices, we show that the magnetic field profoundly alters the impurity scattering rate, which now acquires a finite zero frequency value. As a consequence, we predict a Drude-like line shape in the microwave conductivity at low frequency.