Phase diagram of multiply connected superconductors: A thin-wire loop and a thin film with a circular hole

The phase diagram of a thin superconducting film with a circular hole in axial magnetic field is presented. The result is obtained by solving numerically the nonlinear Ginzburg-Landau (GL) equation in the limit of a thin film with large ${\mathrm{\kappa }}_{\mathit{e}\mathit{f}\mathit{f}}$=${\lambda }_{\mathit{e}\mathit{f}\mathit{f}}$/ξ (where ${\lambda }_{\mathit{e}\mathit{f}\mathit{f}}$=${\lambda }^2$/d is the effective screening length for a film of thickness d). First-order phase transitions between localized (around the hole) superconducting states with different orbital momenta are predicted. Corresponding jumps in the magnetic moment, latent heat, and specific heat are presented in the universal form. The same problem is solved analytically for a thin-wire superconducting loop. All the results obtained for a film with a circular hole are valid for high-${\mathit{T}}_{\mathit{c}}$ superconductors with columnar defects because in such compounds the GL parameter κ∼100 so the screening effect is negligible: a relative distortion of the phase diagram after taking into account the screening effect is proportional to 1/${\mathrm{\kappa }}^2$ in the three-dimensional case and 1/${\mathrm{\kappa }}_{\mathit{e}\mathit{f}\mathit{f}}$ in the case of a thin film.