Ultrasonic attenuation in d-wave superconductors

We consider a BCS-like model of interacting electrons on a square lattice. Within mean field theory, our model has an instability towards the formatio n of a d-wave superconducting state. We calculate the longitudinal ultrason ic attenuation rate in the superconducting phase in the clean limit for par ameters appropriate to the cuprates. We find that the temperature dependenc e of the attenuation rate is similar to that observed in conventional super conductors for phonon wavevectors along the direction of the antinodes of t he gap. However, the attenuation rate for phonon wavevectors along the noda l direction is found to be strikingly different in its temperature and dopi ng dependence. The attenuation rate as(T) increases in magnitude and shows a sign change in its curvature (when plotted as a function of temperature) with increasing value of dopant concentration.