Critical Fields of mesoscopic superconductors

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Recent measurements have shown oscillations in the upper critical field of simply connected mesoscopic superconductors. A quantitative theory of these effects is given here on the basis of a Ginzburg-Landau description. For small fields, the H-T phase boundary exhibits a cusp where the screening currents change sign for the first time thus defining a lower critical field Hc₁. In the limit where many flux quanta are threading the sample, nucleation occurs at the boundary and the upper critical field becomes identical with the surface critical field Hc₃.