The Connectivity of a Manifold and Quantization of Magnetic Flux

Abstract

If a ring in a superconducting state is placed in a magnetic field and then the field is turned off, a superconducting current will begin to flow in the ring. In striking fashion, it turns out that the magnitude of magnetic flux is quantized, that is, it takes on only values from the discrete set of numbers cnh/2e, n = 0,1, 2, ..., where h is Planck’s constant, e is the charge of an electron, and c is the speed of light. In the case of continuous superconductivity, the flux is equal to zero. This result follows from the macroscopic theory of superconductivity, supplemented by the concept of the Cooper pairing of electrons. This result, discovered by the American physicist Leon Cooper, is the basis of the contemporary microscopic theory of superconductivity, established by J. Bardeen, L. Cooper, and J. Schrieffer in 1957 (the BCS theory, for which the three received the 1972 Nobel Prize).