An experimental and theoretical study of the relation between magnetic field and current in a superconductor

The penetration depth, λ, in superconducting tin at 0° K has been found to be capable of variation by the addition of impurity, 3% of indium causing it to be nearly doubled, although the thermodynamical properties such as T c are hardly affected. It is suggested that this result throws doubt on the phenomenological theory of F. and H. London, and a new equation for the supercurrent is proposed, in which the current is related to an average of the vector potential over a region around the point considered. The size of the region is governed by a parameter ξ, which is dependent, in a similar way to the mean free path in a normal metal, on the degree of purity . The new theory agrees in a satisfactory manner with the experimental results, and also provides an explanation of the magnitude of λ in a pure metal. It has been found that the unusual anisotropy of λ in pure tin is absent in tin + 3 % indium , and this too is in agreement with the prediction of the new theory. The fact that the temperature variation of λ appears to have the same form independent of the degree of purity implies that ξ depends on temperature in the same way as λ; this result agrees with the observed behaviour of the interphase surface energy, α ns , if ξ is regarded as determining the width of the interface between superconducting and normal regions. The paper ends with a discussion of the relation of the new theory to microscopic theories of superconductivity.