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...

We present an experimental study of the diffusive transport in a normal metal near a superconducting interface, showing the reentrance of the metallic conductance at very low temperature. This new mesoscopic regime comes in when the thermal coherence length of the electron pairs exceeds the sample size. The reentrance is suppressed by a bias voltage given by the Thouless energy and can be strongly enhanced by an Aharonov-Bohm flux. Experimental results are well described by the linearized quasiclassical theory. [S0031-9007(96)01817-0] PACS numbers: 74.50.+r, 73.20.Fz, 73.50.Jt, 74.80.Fp During the past few years, the proximity effect between a superconductor (S) and a normal (N) metal has met a noticeable revival, thanks to spectacular progress in the fabrication of samples of mesoscopic size [1]. Experimental study of the transport near a S-N interface has shown that the proximity effect strongly affects electron transport in mesoscopic S-N systems: The deviation DG of the conductance from its normal-state value depends strongly on temperature T and oscillates in an applied magnetic field H if a N loop is present [2][3][4]. Various theoretical approaches were suggested to explain this behavior. A scattering matrix method based upon the Landauer formula [5] as well as a numerical solution of the Bogolubov-de Gennes equations [6] were used. These studies demonstrated that superconductivity does not affect the charge transfer in the N metal if the temperature T and the voltage V are zero, i.e., DG is zero at zero energy. A more powerful method based on the equations for the quasiclassical Green's functions [7-10] was used to obtain the dependence of DG on T and V. It has been established [9] that at V 0 the deviation of the conductance DG increases from zero at T 0 (if electron-electron interaction in N is negligible) with increasing T, reaches a maximum at approximately the Thouless temperature e c ͞k B hD͞k B L 2 , and decreases to zero at T ¿ e c ͞k B . This constitutes the reentrance effect for the metallic conductance of the N metal. Similar dependence of DG͑V ͒ at T 0 has been found in [10] both in a numerical solution of the Bogoliubov-de Gennes equations and in an analytical solution of the equations for the quasiclassical Green's functions.The physics behind this reentrance effect involves nonequilibrium effects between quasiparticles injected by the N reservoirs and electron pairs leaking from S. At the N-S interface, and incident electron is reflected into a hole of the same energy e compared to the Fermi level E F , but with a slight change in wave vector dk due to the branch crossing: dk͞k F e͞E F , k F being the Fermi wave vector. The phase conjugation between the electron and the hole results in a finite pair amplitude involving states ͑k F 1 e͞hy F , 2k F 1 e͞hy F ͒, y F being the Fermi velocity. Such a pair maintains coherence in N up to the energy-dependent diffusion length L e ph D͞e [7,11] which coincides with the well-known thermal length L T ph D͞k B T at e 2pk B T . In the high-temperature...

We have measured the ground state of ferromagnetic Josephson junctions using a single dc SQUID (superconducting quantum interference device).We show that the Josephson coupling is either positive (0 coupling) or negative (pi coupling) depending on the ferromagnetic layer thickness. As expected, the sign change of the Josephson coupling is observed as a shift of half a quantum flux in the SQUID diffraction pattern when operating in the linear limit.

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We have studied hybrid superconducting micro-coolers made of a double SuperconductorInsulator-Normal metal tunnel junction. Under subgap conditions, the Andreev current is found to dominate the single-particle tunnel current. We show that the Andreev current introduces additional dissipation in the normal metal equivalent to Joule heating. By analyzing quantitatively the heat balance in the system, we provide a full description of the evolution of the electronic temperature with the voltage. The dissipation induced by the Andreev current is found to dominate the quasiparticle tunneling-based cooling over a large bias range.PACS numbers: 74.50.+r, 74.45.+c In a tunnel junction between a normal metal (N) and a superconductor (S), the charge transfer occurs mainly through two different mechanisms. The tunneling of a single quasi-particle is possible for electrons or holes with an energy E (compared to the Fermi level E F ) larger than the superconductor gap ∆. At low energy, the charge transfer occurs through the Andreev reflection [1,2]. In the normal metal, an electron (a hole) impinging on the superconducting interface is reflected as a hole (an electron), enabling the transfer of a Cooper pair into (out of) the superconductor. As the energies of the involved electron and hole are located symmetrically around E F , the Andreev reflection does not carry heat through the interface at zero bias. The probability for an incident quasi-particle to follow an Andreev reflection, a specular reflection or a tunnel transfer is given in the ballistic regime (no disorder) by the BTK theory [3]. For a N-I-S tunnel junction with an insulator (I) of intermediate or low transparency, the Andreev reflection probability is predicted to be vanishingly small. Taking into account the quasi-particles confinement in the vicinity of the interface, this is no longer true. This confinement can be induced by the disorder or the presence of a second barrier in the normal metal. A single quasiparticle then experiences several collisions with the interface [4,5]. The actual Andreev reflection transmission coefficient corresponds to the coherent addition of many individual transmission probabilities. Therefore, the Andreev sub-gap current significantly exceeds the ballistic case prediction [6,7] and can be modulated by a magnetic flux [8].A quasi-particle current in a N-I-S junction indeed carries both a charge current and a heat current. With a voltage bias smaller than the gap ∆/e, the tunnel current is selectively made out of high-energy electrons (or holes); this cools the electronic population of the normal metal [9]. In this way, (S-I-N-I-S) micro-coolers based on a double tunnel junction provide a significant temperature reduction which reaches an optimum at a voltage bias just below the gap. At a very low temperature, the thermal transport in such N-I-S tunnel junctions appears to be still little understood. For instance, an apparent reversal of the normal metal temperature evolution was observed in various experiments [10,11] and r...

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A particularly sensitive heat capacity measuring device has allowed us to measure the tunneling process of Mn 12 O 12 -acetate single crystals (mass: 1 and 20 mg) from the irreversible tunneling process below the blocking temperature T B to the reversible resonant tunneling process above T B . Above the T B (typically 3.5 K) we find specific heat anomalies at the magnetic field values that correspond to the crossing of spin up and spin down levels of different magnetic quantum numbers. Below T B , heat relaxation pulses at the crossing of crystal field levels are observed for fields applied antiparallel to the initial magnetization. These measurements give a new scope to Mn 12 O 12 -acetate investigations and show the great interest of nanocalorimetry for studies of big magnetic molecules. [S0031-9007(97)03794-0] PACS numbers: 75.45. + j, 61.46. + w, 07.20.Fw Crystals of Mn 12 O 12 -acetate clusters [1] are molecular spin systems that exhibit spectacular effects [2]. Twelve manganese ions (4 Mn 31 and 8 Mn 41 ) are coupled by ferromagnetic exchange to a S 10 macrospin. The Mn 12 O 12 clusters are embedded in an organic matrix and show no exchange coupling from one cluster to another.The crystals are regular parallelepipeds with a strong magnetocrystalline anisotropy (ϳ60 K) along the longitudinal axis. Once oriented, they present at low temperatures and zero magnetic field a very long relaxation time of the magnetization (two months at 2 K [3]). Recently, quantum tunneling of molecular spins through the anisotropy, at magnetic field values that correspond to the crossing of spin up and spin down levels of different magnetic quantum numbers, has been demonstrated [4][5][6].The anisotropy lifts the 2S 1 1 degeneracy of the magnetic levels in zero field, creating a double well configuration [5] as sketched in Fig. 1. The manganese system is superparamagnetic and can be described by a Hamiltonian of the form [7]where D 0.6 K is the anisotropy energy per cluster, H the magnetic field applied parallel to the easy axis of magnetization, g Ӎ 2 is the gyromagnetic factor, and S is the spin per cluster. H l is a term that does not commute with S z and is due to the demagnetizing field, dipole coupling, higher anisotropy terms, and/or hyperfine splitting. A great effort is underway to understand how it comes about [7,8]. Thermal measurements as a function of a magnetic field enlighten the interplay between the spin system and the lattice of the crystal, e.g., clarifying how the phonons influence the tunneling of the macrospins, therefore, giving a great deal of new information.We have performed two kinds of measurements on Mn 12 O 12 monocrystals, the heat capacity as a function of an applied static magnetic field (C[H]) and the temperature as a function of a slowly scanned magnetic field ͑T ͓H͔͒. The measure of very small single crystals promises a high quality of the sample and avoids the broadening found with powder samples due to the slightly different characteristics of every crystal. On the other side, it implies a gr...

We have studied the diffusion of excess quasiparticles in a current-biased superconductor strip in proximity to a metallic trap junction. In particular, we have measured accurately the superconductor temperature at a near-gap injection voltage. By analyzing our data quantitatively, we provide a full description of the spatial distribution of excess quasiparticles in the superconductor. We show that a metallic trap junction contributes significantly to the evacuation of excess quasiparticles.