Ultrasonic Attenuation in the Vortex State of d-wave Superconductors

TL;DR

This paper calculates how ultrasonic waves are attenuated in d-wave superconductors with vortices, revealing a field-dependent, temperature-independent contribution proportional to the square root of the magnetic field, useful for parameter estimation.

Contribution

It introduces a semi-classical method to compute ultrasonic attenuation in the vortex state of d-wave superconductors, highlighting a field-dependent contribution proportional to √H.

Findings

Attenuation has a temperature-independent component proportional to √H.

The results enable estimation of parameters like v_F, H_c2, or ξ from experimental data.

The method applies in the mixed state at fields between H_{c1} and H_{c2}.

Abstract

We calculate the low temperature quasi-particle contribution to the ultrasonic attenuation rate in the mixed state of d-wave superconductors. Our calculation is performed within the semi-classical approximation using quasi-particle energies that are Doppler shifted, with respect to their values in the Meissner phase, by the supercurrent associated with the vortices. We find that the attenuation at low temperatures and at fields $ H_{c1} \leq H \ll H_{c2}$ has a temperature independent contribution which is proportional to $\surd H$ where $H$ is the applied magnetic field. We indicate how our result in combination with the zero-field result for ultrasonic attenuation can be used to calculate one of the parameters $v_F$, $H_{c2}$ or $\xi$ given the values for any two of them.