Effects of confinement and surface enhancement on superconductivity

Abstract

Within the Ginzburg-Landau approach a theoretical study is performed on the effects of confinement on the transition to superconductivity for type-I and type-II materials with surface enhancement. The superconducting order parameter is characterized by a negative surface extrapolation length b. This leads to an increase of the critical field Hc3 and to a surface critical temperature in zero field Tcs, which exceeds the bulk Tc. When the sample is mesoscopic of linear size L the surface induces superconductivity in the interior for T<Tc(L), with Tc(L)>Tcs. In analogy with adsorbed fluids, superconductivity in thin films of type-I materials is akin to capillary condensation and competes with the interface delocalization or “wetting” transition. The finite-size scaling properties of capillary condensation in superconductors are scrutinized in the limit that the ratio of magnetic penetration depth to superconducting coherence length κ≡λ/ξ goes to zero, using analytic calculations. While standard finite-size scaling holds for the transition in nonzero magnetic field H, an anomalous critical-point shift is found for H=0. The increase of Tc for H=0 is calculated for mesoscopic films, cylindrical wires, and spherical grains of type-I and type-II materials. Surface curvature is shown to induce a significant increase of Tc, characterized by a shift Tc(R)−Tc(∞) inversely proportional to the radius R.

Source-reported materials — not catalogue approval

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