Ultrasonic attenuation and the resistive transition in a superconducting granular lead film

Publisher Website
Google Scholar
Abstract
We present a model for the temperature dependence of the resistance and ultrasonic attenuation of a superconducting granular lead film. Treating the film as a network of random resistors and using percolation methods, we postulate that while the dc resistance is the resistance of an infinite network, the surface acoustic wave measures the average resistance of finite ‘‘subnetworks,’’ the sizes of which are on the order of the acoustic wavelength. The resistance of the infinite network will vanish when more than some critical fraction of the resistors in the network becomes equal to zero. However, when the resistance of the infinite network vanishes, some of the subnetworks will still have nonzero resistance. Consequently, the ultrasonic attenuation should be nonzero even when the dc resistance vanishes. This is in agreement with our experimental data.