Proximity Effect Sandwiches Research Articles

Longitudinal ultrasonic attenuation coefficient for high-T K Kondo superconductors

The ultrasonic attenuation coefficients for longitudinal waves in bulk superconductors containing high-T K Kondo impurities and in proximity effect sandwiches containing the Kondo impurities in the normal layer are obtained using the Matsuura, Ichinose, and Nagaoka approach to treat the scattering by the Kondo impurities. The attenuation coefficients are obtained for temperatures close toT c by suitably renormalizing the propagators and vertices appearing in the leading graphs in the expansion of the density-density correlation function appearing in the definition of the longitudinal attenuation coefficient for the case ql≫1. Closed-form expressions for the attenuation coefficient for the bulk superconductor case are obtained.

Transition temperature and specific heat jump of a proximity effect sandwich containing local spin fluctuations

The renormalization equations for a proximity effect sandwich containing local spin fluctuations in the normal layer are solved when the temperature is close to T/sub x/. Expressions for the transition temperature and the specific heat jump at T/sub c/ are obtained. This decrease of the transition temperature as a function of the thickness of the normal layer is seen in the appropriate limits to be similar to what is expected of sandwiches containing nonmagnetic localized states and of sandwiches containing well-defined magnetic moments. Since no reentrant behavior is seen for the magnetic case, the specific heat jump for this case does not show the increase at low temperatures recently obtained by Kaiser and Keleher for sandwiches containing Kondo impurities.

Theory of proximity-effect sandwiches with magnetic impurities

We extend the theory of proximity-effect sandwiches consisting of a thin normal ($N$) metal in perfect planar contact with a thick superconducting ($S$) metal to the case in which the $N$ metal contains magnetic as well as nonmagnetic impurities. We consider dilute concentrations of antiferromagnetic impurities, adapting the theory of Zittartz, Bringer, and M\"uller-Hartmann for magnetic impurities in superconductors to proximity systems. We discuss the influences of Kondo-effect impurities in this proximity system. We compare our theory with the experimental results of Dumoulin, Guyon, and Nedellec, and suggest possible cases in which new phenomena, such as the presence of three gaps in the density of states, might be observed.

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 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-TK Kondo alloys and high-TK 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-TK 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-TK 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-TK 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.

Penetration depth in proximity-effect superconductors

We have studied magnetic field penetration into the normal-metal side of proximity-effect sandwiches by measuring the periodic magnetic field dependence of the dc Josephson current in tunnel junctions containing the normal-metal/superconductor bilayers. The systems studied include the bilayers Ag/Pb, Al/Pb, Ag/Sn, and Sn/Pb and the trilayer sandwich Ag/Sn/Pb, in the temperature range down to 0.1 K. We find that the magnetic field is screened out of the normal metal in much the same way as for a type-I superconductor, with a penetration depth that becomes independent of the normal-metal thickness, or the temperature, at sufficiently low temperature. The magnitude of the induced normal-metal penetration depth is a function of the normal-metal parameters and the inverse of the gap in the backing superconductor.

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 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.

Proximity effect sandwiches containing nonmagnetic localized states

The effects of resonant scattering by nonmagnetic localized states in the normal layer on the critical temperatures of proximity effect sandwiches are studied through the renormalization of the electron propagators in the McMillan proximity effect model. By treating both the resonant scattering of the normal layer electrons and the Coulomb correlation between electrons of opposite spins located on the same impurity site self-consistently, an expression for the decrease in the critical temperature that shows explicitly the dependences on the parameters that describe the impurity atoms is obtained. The decrease in the critical temperatures as a function of impurity concentration and of normal layer thickness is shown.

Specific heat discontinuity of a proximity-effect sandwich system containing Kondo impurities

The theoretical work of Matsuura, Ichinose, and Nagaoka on the Kondo effect in superconductors and McMillan's tunneling model are applied to a proximity-effect sandwich system containing Kondo impurities. Analytic expressions for the renormalized Green's functions of superconducting and normal-metal electrons are given as functions of the system composition. It is found that as the thicknesses become large, the specific heat discontinuity changes continuously from the Muller-Hartmann-Zittartz value for the magnetic cases to the Ichinose value for the nonmagnetic ones. For small values of the layer thickness, and with the films in proximity, our results can be used to calculate the specific heat jump at the transition temperature numerically.

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 Muller-Hartmann and Zittartz theory for low-Kondo-temperature alloys (Tc≫TK) but deviates from it for high-TK 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.

Transition temperature of proximity-effect sandwich systems containing Kondo impurities

The superconducting proximity effect between thin films of a superconductor and a Kondo alloy is analyzed, using the McMillan tunneling model and the theory of Matsuura, Ichinose, and Nagaoka (MIN). The transition temperature is derived and shown to recover the already known limiting cases: the BCS, McMillan, Mohabir-Nagi, Kaiser, and MIN results. An expression for the effective pair-breaking parameter, different from that of Muller-Hartmann and Zittartz, is obtained and found to contain the terms arising from the impurity effect and the pair-weakening Coulomb repulsion effect.

Tunneling into a superconducting proximity sandwich

Measurements and calculations have been made of the Cooper pair current tunneling into the superconducting side of a proximity effect sandwich.

Theory of Josephson tunneling into proximity-effect sandwiches

We develop the microscopic theory of the superconducting proximity effect to allow the calculation of the Josephson current in tunnel junctions where one or both electrodes are proximity-effect bilayers. The Josephson current can then be calculated with the same theory that is used to interpret quasiparticle tunneling characteristics in quantitative detail. One significant result is that the Josephson current is much more rapidly attenuated by thin normal layers adjacent to the tunnel barrier than is the gap in the quasiparticle current.

Theory of thin proximity-effect sandwiches. II. Effects ofs-wave elastic scattering

We show that Anderson's theorem concerning s-wave elastic scattering is inapplicable to certain types of inhomogeneous superconductors. The example of a proximity-effect sandwich consisting of a thin normal N metal in perfect contact with a thick superconducting (S)metal is considered in detail. The proper treatment of s-wave elastic scattering in the N metal is developed. Previously inexplicable experimental results on tunneling into NS sandwiches are found to be understandable in terms of the theory presented.

Pair-field susceptibility of proximity-effect sandwiches

Measurements of the pair-field susceptibility of Pb-Ag proximity sandwiches in the normal state are quantitatively consistent with a generalized time-dependent Ginzburg-Landau model in which the finite penetration of the barrier between the normal and superconducting films reduces the relaxation frequency of the superconducting fluctuations in a manner similar to the reduction caused by magnetic impurities.

Compound geometrical resonances in superconducting proximity-effect sandwiches

In superconducting-normal-metal sandwich structures in which the pair potential has abrupt spatial changes, Andreev scattering occurs in which electronlike and holelike excitations are intermixed. The Tomasch effect, Rowell-McMillan oscillations, and de Gennes-Saint James bound states result from interference of these excitations within a single film. In this paper we discuss compound resonances which can occur in both films of a sandwich structure in which each film is clean and has a thickness on the order of its coherence length. Two of the compound-resonance effects have the following interpretations: (1) Below the energy gap, the de Gennes-Saint James bound states split into energy bands. (2) Above the energy gap, resonances occurring with different frequencies result in a beating of the oscillations of the density of states as a function of energy. A number of previously puzzling or poorly understood features of published experimental data are shown to be consistent with compound-resonance effects. Suggestions are given for systematic experiments.

Inapplicability of the Anderson theorem to elastic scattering in superconducting proximity effect sandwiches

It is shown that the Anderson theorem does not apply to elastic s-wave scattering in the N metal layer of a proximity effect NS sandwich. For a thin N metal, a consequence of this fact is that the pair potential in the N-metal obeys an equation which is mathematically identical to the equation it satisfies in the phenomenological McMillan tunneling model of the proximity effect. The tunneling density of states for our model differs significantly from the McMillan model predictions, however.

Observation of spin-polarized tunneling in thin proximity-effect sandwiches

Use of a tunneling Hamiltonian model for thin proximity-effect sandwiches in high parallel fields has indicated the possibility of spin splitting the quasiparticle density of states past the point where the up- and down-spin densities of states will cross. This crossing is signified by a large zero-bias peak in the tunneling conductance. In this paper we review the theory leading to this prediction and present the results of spin-polarized tunneling experiments in Al-oxide-Mg-Al junctions. Measurements at 0.4 K on a sandwich with 40 \AA{} of Al over 25 \AA{} of Mg at fields from zero to 3.4 T (where the sandwich went into the normal state) were in qualitative agreement with the theoretical predictions, including the peak at zero bias at the higher field values.

Theoretical investigation of the transition temperature of dirty proximity-effect sandwich systems

The influence of impurities and of an interface barrier on the critical temperature of a superconductor-normal (SN) metal sandwich is studied in the Cooper limit. The investigations are based on new equations which allow us to deal with inhomogeneous, dirty superconducting systems near the critical temperature. In contrast with previous treatments, it is shown that at finite film thicknesses,T c is not only dependent on the N to S thickness ratio, but also on the absolute thickness values, the transmission probability of the interface barrier, and the mean free electron paths. Our results permit the determination of the stay probabilities of McMillan 's tunneling model and the effective length of de Gennes' extended boundary condition on the integral kernel which determinesT c. Finally, it is shown how the conventional Cooper limit result forT c by de Gennes is approached.