Self-consistent solutions of Ginzburg-Landau equations and superconducting edge-suppressed states in magnetic field

Abstract

Self-consistent solutions of the Ginzburg-Landau system of equations, which describe the order parameter and the magnetic field distribution in a long superconducting cylinder of finite radius R, in external magnetic field H, when vortex line, carrying m flux quanta, is situated on the cylinder axis (a giant m-vortex state), are studied numerically. If the field H exceeds some critical value H_s, the giant m-vortex solution becomes unstable and passes to a new stable edge-suppressed form. The quantum number m in this state does not change, but the order parameter diminishes by a jump (almost to zero) near the cylinder surface; however, superconductivity remains in the deep, at some distance from a cylinder axis. This edge-suppressed state exist in the fields H_s<H<H_c, where H_c is the field, in which the second order phase transition into the normal state occures. (In the case of large radii R and finite m the field H_c coincides with critical field H_{c2}, in which superconductivity vanishes in the bulk.) If the vorticity m is large, the edge-suppressed state degenerates into the usual state of surface superconductivity, and may survive up to the field H_{c3}=1.69H_{c2}. The magnetic moment, total magnetic flux, the Gibbs free energies are found, as functions of the field H, for different radii R, vorticities m and parameters κof GL-theory. The intervals of R, κ, m are found, where the edge-suppressed solutions exist. The giant m-vortex states exist in both type-I and type-II superconductors, but the edge-suppressed solutions are possible only in type-II superconductors (with κ> 1/sqrt{2}). The paramagnetic effect in mesoscopic samples and also the possible connection of the theory and experiment are shortly discussed.