The penetration depth and high-frequency resistance of superconducting aluminium

Abstract

Measurements have been made of the surface resistance and reactance of superconducting aluminium, at a frequency of 1200 Mc/s. From the measurements the magnitude of the penetration depth has been deduced. There is evidence that it may be highly anisotropic, but its average value at 0°K may be taken to be 4.9 x 10 -6 cm, which is close to the value found previously for tin. This result cannot be explained by the phenomenological theory of London & London (1935) without introducing as an ad hoc hypothesis a dimensionless parameter supposed to vary widely between the two metals. It is shown that the alternative non-local theory due to Pippard (1953) is not open to the same objection. The high-frequency resistance R of superconducting aluminium has been found to vary with reduced temperature t in a way similar to that of tin. Reasons are given for believing that the similarity is even more extensive, and that the reduced resistance r (= R/R n ) is a universal function of two dimensionless quantities, t and w/w c , for all metals at all frequencies; the characteristic frequency 10c is given approximately by the quantum condition hw c = kT c . The significance of this result is discussed, and two suggestions are offered as to what modifications to the conventional two-fluid model may be needed in order to explain the exact nature of the function. The surface resistance and reactance have also been measured for aluminium in the normal state; their ratio is in good agreement with the theoretical value.