Self-consistent solutions of Ginzburg-Landau equations and   superconducting edge-suppressed states in magnetic field
  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 \kappa of GL-theory. The intervals of R, \kappa, 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 \kappa > 1/sqrt{2}). The paramagnetic effect in mesoscopic samples and also the possible connection of the theory and experiment are shortly discussed. 
G.F. Zharkov, V.G. Zharkov, A.Yu. Zvetkov (P.N. Lebedev Physical   Institute, Moscow, Russia)