McMillan Tunneling Model Research Articles

Effects of aluminum over-layer thickness on characteristics of niobium tunnel junctions fabricated by DC magnetron sputtering

We have fabricated Nb/AlO/sub x//Nb Josephson tunnel junctions using a sputtering apparatus with a load-lock system. The junctions that had 50 /spl mu/m/spl times/50 /spl mu/m area showed a V/sub m/ value (the product of the critical current and the subgap resistance at 2 mV) as high as 50 mV at a current density of 160 A/cm/sup 2/. Moreover, junctions having different thicknesses of the Al overlayer were concurrently fabricated on one wafer to study the dependence of the current-voltage characteristics on this Al over-layer. The I-V characteristics were also calculated by McMillan's tunneling model and were compared with the measured I-V characteristics. >

Transition temperature of proximity-effect antiferromagnetic superconductors sandwiches

The superconducting proximity effect between thin films of antiferromagnetic superconductor (AFS) is investigated using the McMillan tunneling model and the mean field model of AFS given by Nass, Levin and Grest. By assuming the nesting condition for the one-dimensional electron band, the spatial uniformity of the order parameter and the temperature independence of the staggered magnetic field, the transition temperature T c is derived and shown to cover the limiting cases of AFS-normal metal and AFS-superconductor systems. We find that the decrease of T c of the proximity bilayer is due to the proximity induced staggered field in the composite. The results of numerical calculations for T c for various cases are given and discussed.

Single-particle proximity effect between superconductors through a tunneling barrier

The single-particle proximity effect between superconductors seperated by a tunneling barrier is observed experimentally in double tunneling junctions. The dependence of the single-particle proximity effect of a small voltage difference across the tunneling barrier is measured. An energy region  E < Δ appears to be typical for this effect because in this region the proximity-effect-induced superconducting density-of-states function is not smeared. It is possible to describe the single-particle proximity effect between superconductors within the extended McMillan tunneling model of the superconducting proximity effect.

Proximity effect and the thermodynamic properties of superconducting thin films

A straightforward method for the self-consistent solution of the Bogoliubov equations for a class of geometries which includes the case of superconducting thin films is presented. Solutions of the gap equation obtained from the self-consistency condition imposed on the pair amplitude are studied and the temperature and thickness dependence of the gap is obtained. The results obtained are compared, where appropriate, with the corresponding results in Ginzburg-Landau theory and the McMillan tunneling model.

Study on grain boundary Josephson junctions in BaPb1−xBixO3 thin films

Several characteristics have been experimentally investigated for the grain boundary Josephson junctions inherently formed at every grain boundary of polycrystalline sputtered BaPb1−xBixO3 superconducting thin films, where x=0.2, 0.25, and 0.3. The origin of the boundary Josephson junction barrier is ascribed to the low carrier density, the structure sensitiveness, and surface states originating from the Bi ions in the grain boundary region, all of which this superconducting oxide posesses at the same time. The grain boundary Josephson junction exhibits tunneling-type I-V characteristics, which progressively change to those of a weak link in the temperature range near the superconducting transition temperature. The gap voltage observed is less than the value given by the Bardeen–Cooper–Schrieffer theory, except for x=0.3. The temperature dependence of the maximum Josephson current deviates from the Ambegaokar–Baratoff theory in the same temperature range. All these tendencies are interpreted in terms of the McMillan tunneling model for a proximity sandwich, based on a model of a parabolic grain boundary potential barrier. Qualitative agreements are attained for the composition dependence of these characteristics. Relations between the Bi content and the junction barrier properties are also discussed, partly in relation to the strong coupling tendency in this oxide system.

Critical temperature of a proximity junction using Eliashberg theory

We present calculations for the critical temperatureT c of a proximity junction using the McMillan tunneling model but treating the metals on either sides within Eliashberg theory formulated on the imaginary axis. In addition we derive formulas for, and evaluate numerically, the functional derivative ofT c with respect to the electron-phonon spectral density of either side of the junction.

DISCUSSION ON THE SUPERCONDUCTING CRITICAL TEMPERATURE IN A N-S MULTI-FILM STRUCTURE

The McMillan tunneling model has been generalized and applied to a N-S multi-film structure with thickness of each film smaller than the superconducting coherent length. The order parameters and superconducting critical temperature of the structure are calculated, and the possibilities of enhancing Tc by modifying the electron-phonon coupling and contaminating with different atom in the interface regions are also discussed.

Influence of paramagnons on proximity effect tunneling

The theory of superconductor-normal metal thin proximity sandwiches within McMillan's tunneling model is written down for the case when paramagnons are present in the normal side. It is shown that results of proximity effect tunneling experiments in Pd-Pb sandwiches are not inconsistent with a large paramagnon effect in Pd and with the calculated value λ ep = 0.41 for the electron-phonon mass enhancement parameter.

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.

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 Proximity Electrodes with Magnetic Impurities

AbstractStarting from a model of classical spins a proximity electrode with magnetic impurities in the barrier‐near layer is investigated theoretically. The rising differences to the common McMillan tunneling model (MTM), especially, the impurity band in the former gap region of the density of states provide significant changes in the tunneling properties of such a electrode, for example, in all current amplitudes of the Werthamer theory. Detailed investigations of the current‐voltage characteristic for tunnel junctions with proximity electrodes containing magnetic impurities show enhanced excess currents below the sum jump which are qualitative similar to experimental results on tunnel structures with electrodes of Nb or V.

Fluctuation conductivity in a superconducting proximity sandwich

The fluctuation conductivity above the transition temperatureTc is calculated in a superconducting proximity sandwich containing magnetic impurities. The calculations are carried out in the framework of the Kaiser-Zuckermann theory based on the McMillan tunneling model, under the condition τS,NTc≪1, where τS,N are the lifetimes of electrons associated with the tunneling process. The role of the proximity effect is to suppress the fluctuation conductivity by renormalizing the coefficients of the Aslamazov-Larkin and Maki-Thompson terms, and the third term. On the other hand, magnetic impurities affect mostly the Maki-Thompson contribution via the pair-breaking parameter, which is derived as a quantity depending on τS,N, the spin-flip lifetime, and temperature.

A model of proximity effect in thick noble metal clad Nb

Abstract McMillan's tunneling model, together with simple minded second order perturbation theory, is applied to the superconducting proximity effect observed recently by Oda and Nagano in thick Cu clad Nb wires. It is proposed to extend the experiment to thick Au clad Nb wires, in which case one may observe the critical fluctuation in Au around 0.1mK.

Transport properties in a superconducting proximity sandwich. Kondo effect

Temperature-dependent properties are evaluated in a superconducting Kondo alloy induced by the proximity effect. These include (i) the order parameter, (ii) the dc Josephson current, and (iii) the thermal conductivity and ultrasonic attenuation, in the case when there is reentance of superconductivity. The calculations are based on the theory given by Kaiser, in which the McMillan tunneling model and the Mueller-Hartmann-Zittartz theory are combined. The temperature dependence of pair-breaking is reflected directly in the above properties in much the same way as in an intrinsic Kondo superconductor, indicating that proximity-effect studies may provide detailed information on the Kondo effect in superconductivity.

Gneralized McMillan tunneling model of the superconducting proximity effect. Specific heat jump

The reduced specific heat jumps for the superconducting (S) side and the normal (N) side of a strongly coupled N-S composite have been calculated by using the generalized McMillan tunneling model of the superconducting proximity effect. Both cases λ N = 0 and λ N ≠ 0 (where λ N is the BCS interaction constant) have been studied. The results obtained by using the generalized model are significantly different from the ones given by the McMillan tunneling model.

Induced superconductivity in Kondo alloys

The superconducting proximity effect between thin films of a superconductor and a Kondo alloy is analyzed theoretically, using the McMillan tunneling model to describe the proximity effect and the theory of M\uller-Hartmann and Zittartz to describe the effect of Kondo impurities on superconductivity. The calculations are compared to measurements by Dumoulin, Guyon, and Nedellec for $\mathrm{Cu}\mathrm{Cr}$-Pb and other similar systems. Comparison of the tunneling density of states confirms that the bound state moves up towards the band edge more quickly than predicted by the M\uller-Hartmann and Zittartz theory as the Kondo temperature increases. Fitting observed transition temperatures suggests the possibility of reentrant behavior at low temperatures. For both density of states and transition temperature, pair-breaking parameters approximately five times those expected theoretically are required to fit the data, possibly due to orbital degeneracy.

Transport properties in a superconducting proximity sandwich with magnetic impurities

The thermal conductivity and ultrasonic attenuation rate are calculated numerically in a superconducting proximity sandwich containing magnetic impurities on the normal-metal side. The calculations are carried out on the basis of the theory given by Machida, in which the McMillan tunneling model is adopted to describe the proximity effect. In the limit of a thick superconducting film, analytical expressions are obtained near the transition temperature T = T c and near T = 0. As in the case of a bulk superconductor with magnetic impurities, the existence of a bound state within an effective energy gap gives a significant effect on the transport properties. The calculation is compared with experiment on the thermal conductivity for AgMn/Pb sandwiches, and reasonable agreement is obtained between them.

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.

On the electron tunneling study of the superconducting proximity effect in Pb-Cd

We show that the recent experimental data of Toplicar and Finnemore on the superconducting proximity effect in Pb--Cd thin films can be understood within the McMillan tunneling model by using our new transition temperature (T/sub c/) formula and determining the parameters self-consistently. Agreement between the theoretical and the experimental values of T/sub c/, the gap, and the general shape and the height of the electronic density of state N/sub S/(E) curves is very good. In agreement with experiment, we find no low-energy peak in the density of states.

McMillan tunneling model of the superconducting proximity effect. Specific heat jump

The McMillan tunneling model of the superconducting proximity effect has been used to calculate the specific heat jumps on the S side and on the N side of a proximity composite. The case of the BCS interaction constant on the N side, λN being identically zero and the case λN ≠ 0 have both been studied. The detailed dependence of the normalized specific heat jumps on the McMillan parameters γS and γN and on the transition temperature of the composite has been computed. A reasonable agreement between our theoretical values and recent experimental data of Bevolo et al. is obtained.