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The Andreev Reflection is the key mechanism for thesuperconducting proximity effect. It provides phasecorrelations in a system of non-interacting electrons atmesoscopic scales, i.e. over distances much larger than themicroscopic lengths: Fermi wavelength and elastic electronmean free path. This field of research has attracted anincreasing interest in the recent years in part because of thetremendous development of nanofabrication technologies, andalso because of the richness of the involved quantum effects.In this paper we review some recently achieved advances. Wealso discuss new open questions, in particular non-equilibriumeffects and proximity effect in systems with ferromagneticelements.

The transition line of superconducting arrays of holes exhibits a rich field structure due to the interference of superconducting states nucleated at the holes edges. We studied by means of resistance measurements their effect on the T*c(H) line as a function of transverse magnetic field using regular arrays of nanofabricated micron size holes. The arrays transition fields are higher than for the bulk. Moreover we found a nontrivial field modulation of the T*c(H) line with an inversion, with increasing field, of the modulation concavity which we assigned to a crossover from a collective to an isolated edge state regime. The high field regime is well described by the nucleation at a single hole in an infinite film. The modulation at low fields was found to be dominated by the interference of neighbor edge states when the inter-hole distance w becomes comparable to the coherence length ξ(T*c). A comparison between arrays of different hole shape shows the influence of geometry on the type of interaction established, which can described either as a superconducting wire network or as a weak link array.

In a mesoscopic metal in proximity with a superconductor, the electronic conductance is enhanced in a very energy-sensitive way. In this paper, we discuss the spectral conductance of a proximity superconductor from both the theoretical and experimental point of view. The dependence of the spectral conductance on the phase-breaking length, gap of the superconductor and interface transparency is theoretically investigated. We present experimental data on the reentrance of the normal-state conductance at very low temperature and bias voltage. A complete description of the experimental data needs taking into account heating of the reservoirs by the bias current. In addition, we show that the energy sensitivity of the proximity effect enables one to access the energy distribution of the conduction electrons inside a mesoscopic sample.

The authors studied the resistive transition of several 2-D superconducting-wire networks of various coupling strengths, which they characterize in terms of the Kosterlitz-Thouless transition temperature and the ratio {xi}/a of the coherence length to the array period. In the extreme strong-coupling limit where the mesh size is of the order of the zero-temperature coherence length, the superconducting behavior is well described by the mean-field properties of the superconducting wave function. Extending to 2-D array, the 1-D phase-slippage model explains the dissipative regime observed above the Ginzburg-Landau depairing critical current. On the other hand, when the coupling is weak, phase fluctuations below the Ginzburg-Landau transition and vortex depinning dominate the resistive behavior. An activated dissipation is observed even below the depairing critical current. Results obtained in this regime for critical temperature, magnetoresistance, or critical current versus temperature, and magnetic field are shown; their periodic oscillations are discussed in terms of depinning of vortices on the array. A simple periodic pinning potential for a vortex in a wire network is calculated, and compared with the case of pinning in Josephson junction arrays. It is shown that this model explains qualitatively the experimental results observed for small {xi}/a.

The numerical result of U[sub kin] = 9.9 E[sub J] at [Phi]/[Phi][sub 0] = 1/2 should be replaced by 2.63 E[sub J] in Sec. 5.1, paragraph 4, in Sec. 5.2, paragraphs 2 and 3, and in Appendix A, the last paragraph. Accordingly, the value of [Delta]U[sub kin] = 6.2 E[sub J] should be replaced by U[sub kin] = 0.17 E[sub J] in Sec. 5.2, paragraph 4. This lower value of the kinetic energy barrier does not significantly affect the conclusions of the paper. It actually improves the agreement with the experimental data in the low temperature range (Appendix B), but the authors still tend to overestimate the oscillation of the periodic pinning potential at higher temperature, as discussed in Sec. 5.2 of the paper.