Properties of an Abrikosov Fluxoid in Type-II Superconductors

An Abrikosov fluxoid in a pure, bulk, type-II superconductor has been studied by the Green's-function technique for superconductors, as developed by Gor'kov. An approximate Green's function has been obtained for the system, and the local densities of states have been evaluated numerically as a function of energy and position in the fluxoid. In agreement with the results of Caroli, de Gennes, and Matricon, the calculated density of states near the Fermi surface is comparable to that of a cylinder of normal metal with radius ξ₀, the coherence distance. The effect of fluxoids on the nuclear spin relaxation rate of a superconductor has been estimated from these results. For fairly high temperatures, the relaxation rate of a superconductor with fluxoids is less than the rate for the same superconductor in zero field, while for very low temperatures, the rate is increased. These trends are in agreement with the experimental data of Silbernagel.