Ginzburg-Landau calculations for a superconducting cylinder in a magnetic field

Abstract

Self-consistent solutions of the Ginzburg-Landau system of nonlinear equations, which describe the behavior of the order parameter ψ and the magnetic-field distribution B in a long superconducting cylinder of finite radius R in external magnetic field H, provided that, there are no vortices inside the superconductor, are studied by using numerical method. The lower and upper critical fields of the cylinder, Hc1(0) and Hc2(0), are found as functions of the radius R, temperature T, and parameter κ of the Ginzburg-Landau theory. For type-I superconductors one has Hc1(0)=Hc2(0); for type-II superconductors one has Hc1(0)<Hc2(0). In small fields H<Hc1(0) the superconductor is in stable Meissner phase (with ψ∼1 and B∼0). It is found, that for type-II superconductors the state with ψ∼1 is unstable in the fields H>Hc1(0), and the superconductor passes to a new stable state. In this state the external field begins to penetrate freely into a superconductor in a form of a finite width ring, which is situated near the surface of the cylinder, where the order parameter is strongly suppressed (the rim-suppressed state). The field Hc1(0) differs from the lower critical field Hc1, at which the field begins to penetrate into the bulk superconductor in a form of vortices. When the field H is increased further, this ring layer (or, the rim) widens, while the order parameter remaines finite (ψ≠0) only near the center of the cylinder. In the field H=Hc2(0) the order parameter finally vanishes everywhere and the metal passes into the normal state. For R≫λ the field Hc2(0) coincides with the upper critical field Hc2, at which the mixed vortex state terminates. The intervals of R, T, and κ, where the rim-suppressed state can exist, are found.

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