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

TLDR

The study proposes a new supercurrent equation that challenges London’s phenomenological theory and discusses its connection to microscopic superconductivity models. The proposed equation relates current to the average vector potential over a region whose size, governed by a purity‑dependent parameter ξ, mirrors the mean free path in normal metals. Experimental measurements show that adding 3 % indium nearly doubles tin’s penetration depth λ without affecting Tc, and the new theory accurately reproduces λ’s magnitude, anisotropy disappearance, and temperature‑independent variation, consistent with interphase surface energy behavior.

Abstract

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.