We carry out an extensive experimental and theoretical study of the Josephson effect in S-N-S junctions made of a diffusive normal metal ͑N͒ embedded between two superconducting electrodes ͑S͒. Our experiments are performed on Nb-Cu-Nb junctions with highly transparent interfaces. We give the predictions of the quasiclassical theory in various regimes on a precise and quantitative level. We describe the crossover between the short-and the long-junction regimes and provide the temperature dependence of the critical current using dimensionless units eR N The Josephson effect is well known to exist in weak links connecting two superconducting electrodes S, e.g., a tunnel barrier I, a short constriction C or a normal metal N ͑S-I-S, S-C-S, and S-N-S junctions͒. This effect manifests itself in a nondissipative dc current flowing through the Josephson junction at zero voltage. At weak coupling, e.g., in the S-I-S case, the Josephson current can be expressed as I s ϭI c sin , where is the phase difference between the two superconducting condensates and the maximum supercurrent I c is called the critical current.The Josephson effect in S-N-S junctions has been studied in a variety of configurations. The early experiments of Clarke 1 and Shepherd 2 were performed in Pb-Cu-Pb sandwiches. In these experiments and in the pioneering calculations by de Gennes, 3 it was already realized that the presence of a supercurrent in such structures is due to the proximity effect. This can be understood as the generation of superconducting correlations in a normal metal connected to a superconductor, mediated by phase-coherent Andreev reflections at the S-N interfaces. The critical current I c is limited by the ''bottleneck'' in the center of the N-layer, where the pair amplitude is exponentially small: I c ϰe ϪL/L T . Here, L T ϭͱបD/2k B T is the characteristic thermal length in the diffusive limit and L is the length of the junction. These calculations, as well as those by Fink, 4 analyzed the temperature dependence of I c within the Ginzburg-Landau theory in the vicinity of the superconducting critical temperature T c . Later, the critical current of diffusive S-N-S microbridges 5,6 was successfully described by Likharev 7 with the aid of the quasiclassical Usadel equations. 8 In this work, the emphasis was put on the high-temperature regime where the superconducting order parameter is smaller than the thermal energy ⌬Ӷk B T. A more general study of the Josephson effect in diffusive S-N-S junctions was made in Ref. 9.More recently, experimental data on long Josephson junctions 10 showed a surprising temperature dependence, which turned out to be in a strong disagreement with the early theory by de Gennes. These data have been discussed by some of us 11 within the quasiclassical approach, which we will also use in the present work. Fink 12 attempted to analyze the data 10 by means of an extrapolation of the GinzburgLandau theory to low temperatures.The proximity effect in mesoscopic hybrid structures consisting of normal and superc...

We present an experimental study of the transport properties of a ferromagnetic metallic wire (Co) in metallic contact with a superconductor (Al). As the temperature is decreased below the Al superconducting transition, the Co resistance exhibits a significant dependence on both temperature and voltage. The differential resistance data show that the decay length for the proximity effect is much larger than we would simply expect from the exchange field of the ferromagnet. 74.50.+r, 74.80.Fp, 85.30St Superconducting proximity effect consists in inducing superconductive properties in a non-superconducting metal. Although this effect has been studied for a long time 1 , it has gained some renewed interest due to recent experiments performed on samples of mesoscopic size. In such samples, the electron phase-breaking length L ϕ is larger than the sample length L. One can thus probe experimentally the characteristic energy scale of the proximity effect ǫ c =hD/L 2 , which is the Thouless energy related to the sample length. This has led for instance to the observation of large magnetoresistance oscillations in normal metal (N) loops in contact with a superconducting (S) island 2-4 . These oscillations provide a direct evidence for the long-range (up to L ϕ ) nature of the proximity effect. Another recent and striking result is the reentrant behaviour. The excess conductance induced by proximity effect is maximum at a temperature or a bias voltage equivalent to the sample Thouless energy 5 , but the normal state conductance reappears at lower energy.Most experiments were performed in noble metals or semiconductor 2D electron gas, where electron interactions are negligible. In a free electron model, the zerotemperature, zero-bias resistance of a mesoscopic metallic wire is predicted to recover the normal state value 6-8 . In the presence of interactions, theoretical studies 7,9 predict a severe modification of the transport properties. Attractive (respectively repulsive) electron-electron interactions are believed to result in a resistance lower (respectively higher) than the normal-state one 7 . This could provide a probe for interactions in normal metals like Au, Ag, etc 10 . In this communication, we present an experimental study of the superconducting proximity effect in a ferromagnetic metal (F). Magnetic metals are in the strong interaction limit. Exchange interactions between electrons in a ferromagnet usually lead to efficient Cooperpair breaking in F-S structures. However, it is worthwhile re-examining the actual proximity effect in a small ferromagnetic wire 11 . Some experiments 12,13 suggested long-range coherence effects, but without any clear conclusion.

We identify the different contributions to quantum interference in a mesoscopic metallic loop in contact with two superconducting electrodes. At low temperature, a flux-modulated Josephson coupling is observed with strong damping over the thermal length LT . At higher temperature, the magnetoresistance exhibits large h/2e-periodic oscillations with 1/T power law decay. This flux-sensitive contribution arises from coherence of low-energy quasiparticles states over the phasebreaking length Lϕ. Mesoscopic fluctuations contribute as a small h/e oscillation, resolved only in the purely normal state.PACS numbers: 74.50.+r, 74.80.Fp, 73.50.Jt, 73.20.Fz In a disordered metal at low temperature, electronic coherence persists over the phase-breaking length L ϕ [1]. Weak localization, which consists in electron coherent backscattering along a closed diffusion path, induces corrections of the conductance of order the quantum of conductance e 2 /h. The sensitivity of this process to an Aharonov-Bohm flux leads to φ 0 = h/2e periodic oscillations of the resistance of a mesoscopic loop [2,3]. Hybrid systems made of Normal (N) and Superconducting (S) materials are the scene for new physics, due to the Andreev reflection and the proximity effect. At low temperature (k B T ≪ ∆), incident electrons have an energy much smaller than the gap ∆ of S and are Andreevreflected at the N-S interface into a coherent hole. Spivak and Kmelnitskii investigated the effect of Andreev reflection on weak localization in a S-N-S geometry [4]. The N metal conductance was predicted to be sensitive to the phase difference between the two superconductors with a period of π, leading to a h/4e flux-periodicity in a loop. Petrashov et al. [5] and de Vegvar et al.[6] measured phase-sensitive transport in mesoscopic N-S metallic systems. The interpretation of Ref.[5] results in terms of weak localization is not consistent with the large amplitude of the effect [7]. In fact, the proximity effect in such mesoscopic systems can lead to a zero-resistance state with a well-defined Josephson current [8] if N-S interfaces have high transparency. In a two-dimensional electron gas, Dimoulas et al. also observed, beyond the Josephson coupling, large effects of quasiparticle interference on the resistance [9]. Recently, there has been considerable interest in coherent transport through mesoscopic N-S tunnel junctions [10,11]. Confinement of electrons and holes by disorder in N induces coherent multiple Andreev reflections, which enhance the low-temperature subgap conductance [12]. This is exemplified by the flux-modulation of the subgap current in the case of a fork-shaped S electrode [13]. Volkov showed that this behaviour may be explained by the appearance, despite the barrier, of a small pair-amplitude in N [14]. This suggests that the proximity effect could explain most of the surprising data on resistive transport in mesoscopic N-S devices, even if classical estimates fail to agree with experimental results.At present, a clear identification of the different c...

This Letter reports measurements of the magnetic field dependence of the resistive critical temperature T c of a regular square network of superconducting aluminum. We find new effects of flux quantization corresonding to both integral (1,2,3,...) and fractional (T>T>T>T>T>T>T) numbers of flux quanta per unit cell of the network. The fractal fine structure of the upper critical-field line is identified as the edge of the Landau-level spectrum for a tight-binding problem on a square lattice.

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The specular reflectivity of lamellar gratings of gold with grooves 0.5 microns wide separated by a distance of 3.5 microns was measured on the 2000 cm −1 -7000 cm −1 spectral range for p-polarized light. For the first time, experimental evidence of the excitation of electromagnetic surface shape resonances for optical frequencies is given. In these resonances the electric field is highly localized inside the grooves and is almost zero in all other regions. For grooves of depth equal to 0.6 microns, we have analyzed one of these modes whose wavelength (3.3 microns) is much greater than the lateral dimension of the grooves.PACS numbers: 71.36.+c, 73.20.Mf, 78.66.Bz Metallic gratings can exhibit absorption anomalies [1]. One of these anomalies which is particularly remarkable is observed for p-polarized light only, and is due to surface plasmon polariton (SPP) excitations. SPP excitation induces a minimum on the specular reflectance spectra which is indicative of the amount of energy flowing parallel to the surface. In a first order approximation, the spectral position of the minimum does not depend on the shape or the amplitude of the grooves but depends only on the dielectric constant and period of the grating. One interesting problem which has been raised long time ago and which is still of interest today is the near field dependence of these modes on the grating shape [2]. Linked to this problem is the possible existence of modes localized in grooves of prominent shape and their relation with non-linear optical effects observed in certain rough metal surfaces [3][4][5][6][7][8].At the beginning of the century Rayleigh pointed out that flat rigid surfaces with cylindrical holes can present acoustic resonances for well defined depths of the holes [9]. Rayleigh showed that under these resonant conditions the acoustic energy is concentrated in the holes and he suggested that similar effects could occur with light. More recently Rendell and Scalapino [10] suggested the possible existence of localized plasmons in order to explain light emission in metal-oxide-metal structures. These plasmon modes are qualitatively different from propagative SPPs on a flat surface excited by attenuated total reflection or by a gentle surface corrugation. Despite the conceptual and practical interest of these surface shape resonances and well documented theoretical predictions, till now no experimental evidence of these electromagnetic resonances has been reported for optical frequencies.In this letter we show that for lamellar gratings with deep rectangular cross sections, localized waveguide resonances which are equivalent to the acoustic resonances described by Rayleigh, can be excited in the channels when the impinging light has an electric field component perpendicular to the grooves direction. The experiments here presented also illustrate the existence of hybrid modes, combination of standing waves localized in the grooves with propagating SPPs.Measured samples consist in periodic arrays of metallic grooves of nominal width ...

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The interplay between superconductivity and Coulomb interactions has been studied for more than twenty years now 1-13 . In low-dimensional systems, superconductivity degrades in the presence of Coulomb repulsion: interactions tend to suppress fluctuations of charge, thereby increasing fluctuations of phase. This can lead to the occurrence of a superconducting-insulator transition, as has been observed in thin superconducting films 5,6 , wires 7 and also in Josephson junction arrays 9,11-13 . The latter are very attractive systems as they enable a relatively easy control of the relevant energies involved in the competition between superconductivity and Coulomb interactions. Josephson junction chains have been successfully used to create particular electromagnetic environments for the reduction of charge fluctuations [14][15][16] . Recently, they have attracted interest as they could provide the basis for the realization of a new type of topologically protected qubit 17,18 or for the implementation of a new current standard 19 . Here we present measurements that show clearly the effect of quantum phase slips on the ground state of a Josephson junction chain. We tune in situ the strength of quantum phase fluctuations and obtain for the first time an excellent agreement with the tight-binding model initially proposed by Matveev et al. 8 .The Hamiltonian for the theoretical description of superconducting circuits can be conveniently obtained by applying Devoret's circuit theory 20 . Here, each electrical element such as an inductance, a capacitor or the Josephson element can add a degree of freedom. In the case of circuits with a small number of electrical elements, a complete analytical description that takes into account all degrees of freedom can be obtained. However, when the circuits contain an increasing number of elements, as for example Josephson junction chains, even numerical solutions of the problem become difficult to obtain when taking into account all degrees of freedom. Nevertheless our measurements demonstrate that the ground state of a phase-biased Josephson junction chain (see Fig. 1(a)) can be described by a single degree of freedom. Although the chain is a multi-dimensional object, the effect of quantum phase-slips can be described by a single variable m, that counts the number of phase-slips in the chain.We start by giving a short introduction on the lowenergy properties of a Josephson junction chain which have been studied in terms of quantum phase slips by Matveev et al. 8 . Let us consider the Josephson junction chain depicted in Fig. 1(a). The chain contains N junctions and is biased with a phase γ. We denote E J the Josephson energy of a single junction and E C = e 2 2C its charging energy. Here we consider E J E C . Let Q i be the charge on each junction and θ i the phase difference. In the nearest-neighbor-capacitance limit the Hamiltonian can be written as:Ignoring the charging energy for the moment, we find the classical ground state, that satisfies the constraint on the phase N i=1 θ i ...