Ultrasonic attenuation in the vortex state of d-wave superconductors

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 less than or equal to H much less than H-c2 has a temperature independent contribution which is proportional to rootH 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 nu(F), H-c2 or given the values for any two of them. (C) 2003 Elsevier Science B.V. All rights reserved.