Electromagnetic Attenuation of Transverse Ultrasound in Superconductors

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Abstract
The electromagnetic field set up by a transverse sound wave in a superconductor is screened out by the Meissner effect at temperatures below the transition temperature. Consequently the attenuation produced by electromagnetic coupling to the quasiparticles undergoes an abrupt decrease below the transition temperature. At sufficiently high frequencies the wavelength is short enough that this "rapid fall" is spread out over an appreciable temperature range. Thus measurements of the rapid fall in electromagnetic attenuation can provide a test for theories of the temperature dependence of screening in the superconducting state. Such measurements would have an advantage over the usual penetration-depth measurements in that they would study the response of the superconductor to a pure sinusoidal wave and not to an integrated superposition of such waves. But the analysis of the data requires a reliable theoretical expression for the transverse conductivity in the superconducting state. This is computed in the present paper from the BCS theory along straightforward conventional lines. It is noted that the relevent coherence factors are the same as in the problem of nuclear spin relaxation, and that a logarithmic divergence due to the confluence of the singular density-of-states functions also enters in the present problem. In the present case this divergence is cut off by the finite frequency of the quasiparticle transition. For sufficiently high frequency this anomalous behavior of the transverse conductivity function can result in a "rapid rise" in the transverse attenuation immediately below the transition temperature, before the rapid fall sets in from screening.