Ultrasonic attenuation in an orthorhombic anisotropic superconductor

We show that ultrasound attenuation in a clean two-dimensional orthorhombic superconductor can be used to get information separately, on band-structure anisotropy, and on the relative magnitude of a subdominant s-wave component to the dominant d-wave gap. An angular sweep as a function of orientation of the in-plane attenuated sound momentum will exhibit a twofold pattern. Using a simplified one-band model of the electronic structure with anisotropic effective masses in the plane, we illustrate that the maximum in the attenuation occurs when the direction of the sound is perpendicular to the direction of the Fermi velocity at the nodes. This is not the same as the direction of the nodes in the gap except for the case of a circular Fermi surface. Nevertheless, with the same analysis, nodal directions can be determined as well as band and gap anisotropy parameters and the ratio of gap magnitude to Fermi energy.