Attenuation of Longitudinal Acoustic Waves in Type-II Superconductors

Abstract

The attenuation of longitudinal sound waves in a superconductor with a spatially dependent energy gap is studied by a Green's-function method. In order that explicit expressions for the ultrasonic loss may be derived, the calculation is restricted to temperatures $T\sim T_c$, the transition temperature. The results of the calculation are used to study ultrasonic attenuation in a type-II superconductor near $T_c$, which contains a low density of flux lines, $H\sim H_{c_1}$. It is assumed that under these conditions the flux tubes in the material are fixed, are well separated, and form a periodic array. It is then shown that not only is the attenuation anisotropic, but anomalous absorption or transmission takes place whenever the sound wavelength matches the distance between vortices. Although the above theory is only for $T\sim T_c$ and $H\sim H_{c_1}$, it is expected that this effect will exist over wider ranges of temperature and magnetic field, and, if accessible to experiment, will yield a direct measure of the spacing of flux lines in type-II superconductors.