Surface superconducting states and paramagnetism in mesoscopic superconductors

In the framework of the Ginzburg-Landau equation, the temperature dependence of the upper critical field of small ring-like superconductors is studied. At equilibrium small parts of the phase diagram show paramagnetism for width / radius ratios below 0.85. Their number and extension increase with the size of the hole. In these regions, only the inner part of the ring shows a positive magnetic moment. The order parameter density profile appears to change, when crossing a first order transition line, which separates different angular momentum values, and we clarify the relationship between the localization of superconductivity nucleation and paramagnetism of those samples.