Proximity effect sandwiches containing local spin fluctuations

A proximity effect sandwich that contains local spin fluctuations in the normal layer is studied. The renormalization group approach is used to treat the Coulomb repulsion between thed electrons of opposite spins that are localized on the transition metal impurities present in the normal layer. The perturbations due to the tunneling of electrons from one layer to the other and the mixing of the normal-layer electrons with the impurityd electrons are treated using the standard Born approximation. A decrease of the transition temperature for both thin and thick, superconducting layers is obtained. It is found that there is a critical concentration at which the superconductivity in the thin superconducting layer can be quenched. For the thick-superconducting-layer sandwiches, no critical concentration is found.     

Proximity effect tunneling into two-band metals containing Anderson impurities

The effect of Anderson impurities on proximity effect tunneling into two-band metals such as palladium is studied. The Yamada-Yosida approach is used to treat the Anderson impurities in the two-band metal. In the Kondo region, it is shown that the pair-breaking parameter for thed band mimics the pair-breaking parameter in the Müller-Hartmann and Zittartz theory for low-Kondo-temperature alloys (T _c?T _K) but deviates from it for high-T _K alloys. The change in the transition temperature of the proximity effect sandwich due to the presence of Anderson impurities in the two bands of the normal side appears to be similar to that obtained by Kaiser except for the presence of the new pair-breaking parameter.     

Proximity effect for superconductors containing transition metal impurities. II

The tunneling conductance is calculated by the use of a theory extending the Kaiser-Zuckermann theory. The superconducting proximity effect in a superconductor-normal metal sandwich system in which the metal on the normal side contains dilute 3d transition metal impurities is taken into account fully. An analysis for experimental results of the tunneling conductance on CuCr backed by Pb is presented. Qualitative agreement between the present calculations and the experimental data is obtained.     

Proximity effect for superconductors containing transition metal impurities. I

The superconducting proximity effect in a superconductor-normal metal sandwich system in which the metal on the normal side contains dilute 3d transition metal impurities is investigated theoretically. The Kaiser-Zuckermann theory, based on McMillan's tunneling model, is extended by the use of the Hartree-Fock version of the Anderson model to give rise to a bound state in an effective energy gap. For the purpose of analyzing experimental results, the transition temperature and the critical concentration for gapless superconductivity are calculated. It is also demonstrated that with increasing impurity concentration, an impurity band merges into a gap, which may correspond to recent experimental findings.     

Critical temperature for a layered superconductor containing nonmagnetic impurities

The critical temperature of a layered superconductor has been calculated using the model of an electron-bosonic pairing. Influence of impurities has been considered using for the bosonic propagator the modified plasmonic propagator. The main result is a decreasing of the critical temperature due to the nonmagnetic impurities. The results are important for the case of high critical temperature superconductors doped with nonmagnetic impurities.     

Transition temperature of superconducting-magnetic proximity effect sandwiches

The diffusion approximation of Werthamer and de Gennes for the calculation ofT _c of proximity effect sandwiches is generalized to include the effect of a barrier with a finite penetration probability.T _c is higher than the one calculated for a transparent barrier. The effect of the barrier enters through generalized boundary conditions for the pair potentials. It is found that within the diffusion approximation, the presence of magnetic impurities on the normal side does not affect the boundary conditions.     

Andreev Reflection and Proximity effect

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.     

Proximity effect in quartz crystal microbalance

When an object approaches a vibrating quartz crystal microbalance (QCM) the resonant frequency changes. This "proximity effect" was seen at the distance of 10 mm in air and became more pronounced as the distance decreased. This effect depends on the quality factor (Q-factor) value of a QCM, conductivity of the object, and electrical connection of the object to QCM electrodes. A special setup was constructed to test the impact of the proximity effect on a QCM. Damping fluid was placed on one side of QCM, to change the Q-factor. A conducting metal disk was brought close to the other side of the QCM exposed to air. By varying the distance between the QCM and an object (metal disk), a shift in frequency was observed. This proximity effect was largest (>200 Hz for 10 MHz QCM) when the Q-factor was low and a conducting metal disk (e.g., Cu) was electrically shorted to the proximal (nearest) QCM electrode. The finite element modeling showed that the proximity effect was likely due to interaction of the object with the fringing electromagnetic field of the QCM. A simple modified Butterworth Van-Dyke model was used to describe this effect. It must be recognized that this effect may lead to large experimental artifacts in a variety of analytical QCM applications where the Q-factor changes. Therefore, in order to avoid artifacts, QCM and similar mass acoustic devices should not operate in the low Q-factor (<1000) regime.     

A Shiba-Rusinov theory for paramagnetic impurities in proximity effect sandwiches

The Shiba-Rusinov theory, which takes into account both the potential and exchange interactions existing between a conduction electron and a paramagnetic impurity atom, is used to study the effects due to paramagnetic impurities dissolved in the normal layer of a proximity effect sandwich. Using aT-matrix approach to treat the interactions due to the impurities and the standard Born approximation to treat the other interactions in the sandwich, we obtain a set of self-consistent equations for the renormalized frequencies and the unrenormalized energy gaps for the electrons in both layers. The solutions of these equations are then used to obtain expressions for the decrease in the transition temperature of the sandwich and for the jump in the specific heat atT _c .     

Proximity effect in gadolinium-backed lead films

Measurements of the surface reactance, at a frequency of 100 MHz and at various temperatures, have been used to study some aspects of the proximity effect in lead films in contact with gadolinium. It has been found that although the normal metal in this case is magnetic an adequate explanation of the experimental results cannot be obtained by assuming that the Ginzburg-Landau order parameter vanishes at theNS interface. The microscopic theory that allows the boundary condition () _n =/b (wheren indicates the normal component of the gradient, is the order parameter, andb is called the extrapolation length) does agree well with both the dependence of the transition temperatureT _cNS on the thickness of the superconducting layer and variation of the surface reactance with temperature.Research supported by the National Science Foundation and the U.S. Army Electronics Laboratory, Fort Monmouth, New Jersey.Part of this work was completed in the Department of Physics, University of California, Berkeley, during the tenure of a Rutgers University Research Council Faculty Fellowship.     

Bifurcation theory and order of phase transition for proximity effect sandwiches

We use bifurcation theory to study the order of the phase transition for inhomogeneous superconducting systems described by the Ginzburg-Landau equations. Complete qualitative information on the behavior near the critical point can be obtained using these techniques of nonlinear analysis and the calculus of variations. We prove in a rigorous way that there is a secondorder phase transition for a normal-superconducting-normal (N-S-N) proximity sandwich. Moreover, in the case of a magnetic-superconductingmagnetic (M-S-M) proximity sandwich we show the dependence of the order of the phase transition on the coupling constant between the magnetic and superconducting order parameters.Partially supported by CNR-GNSM.     

Thermodynamic properties of antiferromagnetic superconductors containing nonmagnetic,magnetic, and spin-orbit impurities

Effects of all types of impurities (nonmagnetic, magnetic, and spin-orbit) on an antiferromagnetic superconductor (AFSC) have been investigated by studying the transition temperatureT _c and the specific heat jump. We have assumed a one-dimensional electron band. The impurity scattering is treated within the self-consistent Born approximation. We find that: (a) the molecular fieldH _Q and the magnetic impurities depress superconductivity of AFSC and their pair-breaking effect is additive; (b) the effect of spin-orbit impurities is the same as that of nonmagnetic impurities—these enhance superconductivity by screening the molecular field; and (c) in the extreme dirty limit, the AFSC is described in terms of an effective pair-breaking parameter given by 1/_eff=1/₂+H _Q ² where 1/=1/₁+2/3_so(1/₁, 1/₂, and 1/_so, respectively, are the scattering rates from nonmagnetic, magnetic and spin-orbit impurities).     

Phonon structure in the tunneling characteristics of thin proximity effect sandwiches

The tunneling spectra of Al-oxide-N-S proximity effect junctions show phonon structure not only from the superconducting layerS, but also from the normal metal layerN. We report experimental results for junctios with Ag, Cu, and Al normal metal layers (100–400 Å thick) and Pb or Sn superconducting layers (3000 Å thick). We compare these experimental results with the McMillan geometrical resonance model of the proximity effect and with an extended McMillan tunneling model. The extension includes the effect of the frequency-dependent electron-phonon interaction in the normal metal. Finally, we estimate the electron-phonon coupling constant for the normal metals from the size of their phonon structure in the tunneling spectra.Research supported by National Science Foundation under Grant #NSF DMR 73-7518 A01.Research supported by National Science Foundation under Grant #NSF DMR 75-19544.Research supported by National Science Foundation under Grant #GH 37239.     

Proximity effect and branching conditions in superconducting networks

The onset of superconductivity on proximity networks made of very thin wires of different materials is investigated by adapting de Gennes' one-frequency approximation for dirty superconductors to networks. Branching conditions for the order parameter in the presence of a magnetic fieldH are derived, and an equation for the global critical temperatureT _c (H) of arbitrary networks is obtained that generalizes Alexander's equation for networks made of a single material. Numerical applications to simple proximity networks are given showing phase boundariesT _c (H) and the order parameter on adjacent branches as a function of geometry and mean free path.     

Energy relaxation during inelastic electron scattering on localized states

A mechanism which can be responsible for the phase relaxation in polycrystalline semiconductors and metals is proposed. This mechanism is related to the inelastic scattering of electrons on localized states with energies near the Fermi level.     

Proximity effect tunneling into high-T K Kondo alloys

The proximity effect tunneling into Kondo alloys is studied within the framework of the Matsuura, Ichinose, and Nagaoka (MIN) theory, which is valid for both low-T _K Kondo alloys and high-T _K Kondo alloys. By working with the two-particle propagators, the effects of both the repulsive interaction arising from the virtual polarization of the impurities in the ground state and the pair-breaking interactions on the decrease in the transition temperatures of the proximity effect sandwich can be clearly seen. It is found that the expression for the decrease for the sandwich containing low-T _K Kondo impurities in the normal layer is similar to the expression obtained by Kaiser except for a redefinition of the pair-breaking parameter. For the high-T _K Kondo impurities, the presence of the additional repulsive interaction in the MIN theory leads to an expression for the transition temperature decrease that is different from those previously obtained. The existence of a critical concentration of high-T _K Kondo impurities in the normal layer at which the superconductivity of the sandwich is destroyed is seen to be directly connected to the presence of the contribution due to the repulsive interaction term in the expression for the decrease in the transition temperature.     

Proximity effect tunneling into virtual bound state alloys

The effects of a narrow virtual bound state formed by transition metal impurities dissolved in the normal layer of a superconducting proximity effect sandwich are studied. Using standard renormalization techniques, we obtain the changes in the transition temperatures and the jumps in the specific heat atT _c as a function of the thickness of the normal layer, of the widths of the virtual bound states, and of the impurity concentrations. It is seen that narrow virtual bound states lead to decreases in the transition temperatures, while broad virtual bound states do not. It is further seen that the narrow virtual bound state causes the reduced specific heat jump atT _c to deviate from the BCS behavior expected of the pure sandwich.     

The effect of oxide surface layers on the breakdown voltage in metal-vacuum-metal sandwiches

Correlations are explored between the observed breakdown voltages in metal-vacuum-sandwiches and the properties of the metallic electrodes which are believed to be covered by oxide layers. A linear relationship is indicated between the work function of the electrode and the breakdown voltage. This relationship may prove useful in obtaining more accurate estimates for the breakdown voltage of the vacuum dielectric itself, when it is sandwiched between a wide variety of electrode materials.     

Experimental verification of localized defect states in Ga-Ge-Se nano colloidal solutions

Linear optical studies on Ga₉Ge₂₇Se₆₄ nanocolloidal solutions were carried out. Evidence for the existence of defect states in these nanoclusters are obtained from absorption spectra, and its occurrence is emphasized by analyzing the fluorescence and thermal diffusivity studies. An intermediate peak in the band tail of the absorption spectrum is observed at high concentration, and it is interpreted as the absorption due to localized defect states. Fluorescence emission corresponding to this peak confirms the same. The thermal diffusivity studies show that nanocolloidal solutions with less solute concentration have high thermal diffusivity. This indicates the existence of high defect states density which increases with the increase in cluster size, leads to scattering of phonons from the defect centers and in turn results in lowering of thermal diffusivity.     

Proximity effect in superconductors: Calculation of the transition temperature

The problem of the calculation of the transition temperature in the proximity effect is considered. From the variational principle of Silvert and Cooper we derive a simpler variational principle which is useful in obtaining a rapid numerical estimate of the transition temperature as well as the qualitative features of the solution. Approximate and exact solutions for the transition temperature and the order parameter are obtained in the clean limit, the geometry investigated being that of a superconducting sphere embedded in an infinite normal matrix. The results for the transition temperature do not display the unphysical behavior found in previous work in the clean limit and suggest that there is a critical radius for the sphere below which the sample is normal at all temperatures. The results for the order parameter show that the nonanalytic behavior discovered by Silvert and Cooper is a relatively small effect in the case investigated.Supported in part by the National Research Council of Canada and in part by Scarborough College, University of Toronto.