The Nature of the Superconducting State. II

Abstract

The discrete levels of the electrons of a metal, lying below the continuum of levels predicted by the energy band theory, and interpreted in an earlier paper as leading to the superconducting state, have been further investigated, though a quantitative discussion in the general case is still impossible. The wave functions correspond to electrons which can wander for some distance through the metal, but are held to a finite region by forces of interaction with positive ions. Such wave functions will carry no current in the ordinary way, for they correspond to the correlation of an electron and a positive ion, and the two move together. On the other hand, being similar to large atoms, they have a large diamagnetism, and hence may perhaps lead to London's form of theory of superconductivity. In the second section, this possibility is discussed. It is shown, by reference to the ordinary theory of diamagnetism, that the two conventional types of theory, one for bound electrons, the other for free electrons, are treated in such different ways that one cannot in all cases interpolate between them. Instead, as wave functions become larger and larger, one can continue to treat them by the method appropriate to isolated atoms, until they become so large that the energy associated with the Larmor precession becomes comparable with the atomic energy. Then the properties change, and the method appropriate to free electrons gradually becomes correct. This limiting size depends on the magnetic field, or conversely the limiting magnetic field depends on the size. It is shown that to produce superconductivity the orbits must be of the order of magnitude of 137 atomic diameters, a not unreasonable figure with our model. Then the limiting magnetic field, above which the large diamagnetism or superconductivity would be expected to disappear, proves to be of the order of a few hundred gauss, or the order of magnitude of fields actually necessary to destroy superconductivity.