The proximity effect in flux pinning

Abstract

The elementary interaction force f_p for a small normal conducting precipitate particle is usually estimated assuming that the entire condensation energy of the superconductor 1/2 μ₀H²_c is lost in the volume of the particle, i.e., that the particle is equivalent to a void. It is demonstrated that this assumption, which neglects the proximity effect, leads to a serious over estimate of f_p, by as much as three orders of magnitude. The ratio of f_p of a normal precipitate to f_p of a void of the same volume is shown to be of the order (t/ξ₀)², where t is the smallest dimension of the particle and ξ₀ is the BCS coherence length. In addition, the ratio is temperature dependent, becoming smaller (larger correction) as T approaches T_c. These predictions are compared with recent experimental measurements of pinning by voids and precipitates and are shown to rationalize some hitherto puzzling experimental discrepancies between pinning by the two types of defects. Application of these ideas to flux pinning by other defects, such as grain boundaries and dislocations, is also discussed.