超伝導入門 第５章 ピパード方程式とコヒーレンス長さ

Abstract

The penetration depth may be measured with refined accuracy by measuring the surface impedance in the microwave region. This technique was utilized by Pippard to measure the change in penetration depth with the application of magnetic fields. He found that the change in penetration depth with the application of fields up to the critical field was on the order of 1%, which indicates that the entropy density change occuring in the transition to the normal state is anomalously large in the penetration depth region. This anomaly may be resolved if it is assumed that there is coherence between super-electrons over a region larger than the penetration depth. In this case, the state of a super-electron at one position cannot be defined by the magnetic field at that position as assumed in the London equation and will feel the change in the magnetic field over the length of coherence. An analogous situation in normal metals occurs when the mean free path of electrons becomes larger than the skin depth as the electron is accelerated by a field which varies with position. Pippard used this analogy to revise the London equation, which takes into account the variation of the vector potential over the coherence length. The derivation of the Pippard equation and its significance are described.