## No full-text available

To read the full-text of this research,

you can request a copy directly from the authors.

It is found experimentally that the critical current in the two-terminal double-barrier Nb/Ai-AlOx-Nb/Al-AlOx-Nb device is considerably larger than the critical current in the bottom junction of the Nb/Al-AlOx-Nb/Al-AlOx-Ta/Nb device of identical planar configuration produced in the same deposition run. Our data suggest that the origin of the phenomena is a direct Josephson coupling between the external electrodes rather than the inductive interaction between the junctions. (C) 1997 Elsevier Science B.V.

To read the full-text of this research,

you can request a copy directly from the authors.

... A double-barrier Josephson junction of a SIS'IS type is fabricated from Nb/Al-AlO -Nb/Al-AlO -Nb/Al structures deposited in the same vacuum with the aim to provide the identical material parameters of the films and the tunnel barriers. In the paper [16], the fabrication procedure is described more in detail. In the paper [2], an absolute value of a Josephson current in a double-barrier Josephson junction with very thin middle electrodes is studied experimentally. ...

The dependence of the current density on the phase difference is investigated considering the layered superconducting structures of a SIS'IS type. To simplify the calculations, the quasiclassical equations for the Green's functions in a \textit{t}-representation are derived. An order parameter is considered as a piecewise constant function. To consider the general case, no restrictions on the dielectric layer transparency and the thickness of the intermediate layer are imposed. It was found that a new analytical expression for the current-phase relation can be used with the aim to obtain a number of previously known results arising in particular cases.

... A double-barrier Josephson junction of a SIS'IS type is fabricated from Nb/Al-AlO x -Nb/Al-AlO x -Nb/Al structures deposited in the same vacuum with the aim to provide the identical material parameters of the films and the tunnel barriers. In the paper [16], the fabrication procedure is described more in detail. In the paper [2], an absolute value of a Josephson current in a double-barrier Josephson junction with very thin middle electrodes is studied experimentally. ...

The dependence of the current density on the phase difference is investigated considering the layered superconducting structures of a SIS’IS type. To simplify the calculations, the quasiclassical equations for the Green’s functions in a t-representation are derived. An order parameter is considered as a piecewise constant function. To consider the general case, no restrictions on the dielectric layer transparency and the thickness of the intermediate layer are imposed. It was found that a new analytical expression for the current-phase relation can be used with the aim to obtain a number of previously known results arising in particular cases.

... A similar dependence was obtained in works [12,13] on the basis of the classical Ohta model [14]. The experimental observation of a non-sinusoidal dependence of the current through a two-barrier superconductor junction was described in works [15,16]. ...

The Josephson current through a two-barrier SISIS tunnel junction has been calculated analytically in the quasiclassical approximation for the microscopic theory of superconductivity. Green’s functions for a SISIS tunnel junction and an expression for the Josephson current through a point contact are obtained. The dependence of the tunnel current on the order parameter phase is determined, and the current dependence on the distance between the barriers is analyzed. The presence of resonance peaks in the Josephson current is demonstrated.

Current-voltage characteristics of triple-barrier Josephson junctions are analytically and numerically studied. In the presence of a constant current bias and for homogeneous Josephson coupling of all layers, these systems behave exactly as ordinary Josephson junctions, despite their non-canonical current-phase relation. Deviation from this behaviour is found for inhomogeneous Josephson coupling between different layers in the device. Appearance of integer and fractional Shapiro steps are predicted in the presence of r. f. frequency radiation. In particular, the amplitudes of these steps are calculated in the homogeneous case as clear footprints of the non-canonical current-phase relation in these systems.

A generalization of the semi-classical model describing the Josephson dynamics of tri-layer superconducting systems is given by assuming a constant non-null arbitrary superconducting phase for the inner electrode and the presence of inhomogeneities in the superconducting coupling between electrodes. Extension of the model to triple-barrier Josephson junctions is proposed. Integer and fractional Shapiro steps are predicted and their amplitudes are calculated.

The current-phase (I-ω) relation of a double-barrier Josephson junction with a two-gap superconductor as intermediate electrode is derived by means of a simplified version of Ohta's model. As in conventional double-barrier Josephson junctions, a marked skewness in the I-ω curves is present. Moreover, as in heterotic Josephson devices, a reduction of the maximum Josephson current is predicted. An appropriate experiment to verify the rich behavior of this type of Josephson device is suggested. © 2013 EDP Sciences, Società Italiana di Fisica, Springer-Verlag.

It was observed experimentally that the magnitude of the Josephson current through a single junction in the double-barrier Nb/Al-AlOâ-Nb/Al-AlOâ-Nb stack is lower than that for the whole device. This effect is explained by a model that takes into account Andreev reflection in the S-I-S{sup â²}-I-S double-barrier stack, where S and S{sup â²} are superconductors and I is an insulator. The middle S{sup â²} layer is very thin (with the thickness of order the coherence length) and has reduced superconducting parameters as compared with the external S layers. The model predicts bound state levels in the middle electrode. The bound states provide an additional channel of Josephson tunneling which results in enhanced Josephson critical current density through the stack as compared with that for the single S-I-S{sup â²} junction. {copyright} {ital 1999} {ital The American Physical Society}

The Hamiltonian of a superconducting thin loop interrupted by a double-barrier Josephson junction is derived. The parameter epsilo, which takes account of the difference in the Josephson coupling of the two single junctions in the SISIS structure, is seen to allow variation of the energy gap DeltaE01 between the ground state and the first excited flux number state of the system. An additional parameter gamma, describing the coupling between the outer electrodes of the double-barrier Josephson junction, is introduced. Persistent currents in the system are studied in terms of the usual parameter alpha, representing the ratio between the Josephson energy and the magnetic energy, and of the externally applied flux.

The magnetic properties of a rf superconducting quantum interference device containing one overdamped double-barrier junction are studied. The effective nonsinusoidal expression for the current-phase relation with an additional half harmonic term is used for the double-barrier junction. Devices with inhomogeneous double-barrier junctions show a characteristic feature: for fixed and not too high superconducting loop inductance values, transition from irreversible to reversible magnetic behavior can be induced by increasing the difference in the Josephson coupling of the two junctions.

The influence of a constant magnetic field on the maximum Josephson current of a double-barrier junction is studied. Owing to the peculiarity of the current–phase relation of this composite device, the resulting Fraunhofer-like pattern shows an overall enhancement of the maximum Josephson current with respect to the usual single-junction curves for very small difference in the coupling energies of the two pairs of adjacent layers in the system.

Critical currents in a system of two magnetically coupled long Josephson junctions are studied numerically, analytically, and experimentally. We show that the switching from static to dynamic state of one junction can trigger switching of the other, and this process leads to current locking. A distinction is made between different critical currents of an individual junction depending on the static or dynamic state of the other junction. Good agreement between the experiment and numerical simulation is found.

Superconductor–insulator–normal metal–insulator–superconductor (SINIS) and SINS′NIS junctions (here S, I, and N denote superconductor, insulator, and normal metal, respectively) were fabricated using Nb/Al technology and characterized at low temperatures. It is shown that asymmetric SINIS junctions with different transparency of the two tunnel barriers may have higher critical voltages than analogous symmetric junctions at 4.2 K. Also, SINS′NIS junctions were fabricated and investigated. If the thickness of the S′ layer is very thin, these junctions have quasiparticle current–voltage characteristics similar to those of conventional SINIS junctions at 4.2 K, but the Josephson critical current densities, and therefore, the critical voltages, are much higher than the corresponding values for conventional SINIS junctions. © 2001 American Institute of Physics.

An overview of the current status of different types of non-hysteretic Josephson junctions is given with emphasis on double-barrier structures. The results of theoretical work on double-barrier SIS′IS Josephson junctions (I is a tunnel barrier, S′ is a thin film with TC′<TC) are presented. The microscopic model for the supercurrent is developed for two cases: the S′ interlayer in the clean and in the dirty limit. The model describes the cross-over from direct Josephson coupling of the external S electrodes to the regime of two serially connected SIS′ junctions. We calculate the ICRN product as a function of the TC′/TC ratio, the interlayer thickness and the barrier strengths and compare the theory with experimental data for Nb/AlOx/Al/AlOx/Nb junctions. We argue that these junctions are very promising in rapid single flux quantum (RSFQ) and programmable voltage standard applications, since they are intrinsically shunted and have controllable interfaces. We formulate the requirements for materials and interface barriers in order to increase critical current densities and ICRN products in double-barrier junctions.

The transparency of the tunnel barriers in double-barrier junctions influences the critical current density and the form of the current–voltage characteristics (IVC). Moreover, the barrier asymmetry is an important parameter, which has to be controlled in the technological process. We have performed a systematic study of the influence of the barrier transparency on critical current, IC, and normal resistance, RN, by preparing SIS and SINIS junctions under identical technological conditions and comparing their transport properties. We have fabricated Nb/Al2O3/Nb and Nb/Al2O3/Al/Al2O3/Nb devices with different current densities using a conventional fabrication process, varying pressure and oxidation time. The thickness of the Al middle electrode in all Nb/Al2O3/Al/Al2O3/Nb junctions was 6 nm. Patterning of the multilayers was done using conventional photolithography and the selective niobium etching process. The current density of SIS junctions was changed in the range from 0.5 to 10 kA/cm2. At the same conditions the current density of SINIS devices revealed 1–100 A/cm2 with non-hysteretic IVC and characteristic voltages, ICRN, of up to 200 μV. By comparing the experimental and theoretical temperature dependence of the ICRN product we estimated the barrier transparency and its asymmetry. The comparison shows a good agreement of experimental data with the theoretical model of tunneling through double-barrier structures in the dirty limit and provides the effective barrier transparency parameter γeff≈300. A theoretical framework is developed to study the influence of the barrier asymmetry on the current–phase relationship and it is proposed to determine the asymmetry parameter by measuring the critical current suppression as function of applied microwave power. The theoretical approach to determine the non-stationary properties of double-barrier junctions in the adiabatic regime is formulated and the results of calculations of the I–V characteristics are given in relevant limits. The existence and the magnitude of a current deficit are predicted as function of the barrier asymmetry.

In a system of thin alternating layers of superconductors and insulators the equations describing static and dynamic fluxon solutions are derived. The approach, represented by a useful compact matrix form, is intended to describe systems fabricated for example of niobium or niobium‐nitride thin films; in the limit of ultrathin superconductor films it may give a model for describing fluxon motion in layered high‐T c superconductors. Numerical examples of current versus voltage curves to be expected in such an experiment are presented.

The electrodynamics of a metallic surface layer in proximity contact to a superconductor are considered. The surface region is modeled as an idealized proximity-coupled superconductor/normal-metal (S/N) bilayer. Analytical expressions for the magnetic-field penetration into the sample are obtained. The behavior of the model and its applicability to magnetic-screening-length measurements on artificial and naturally occurring S/N bilayer superconductors are discussed in various limits. Calculations of the effective penetration depth lambdaeff(T) reveal that unconventional penetration depth temperature dependences, such as Deltalambdaeff(T)~T found in YBa2Cu3O7-delta crystals, are qualitatively reproduced with this model.

The current-voltage characteristics of N vertically stacked Nb-based long Josephson junctions (N=1,2,3) are measured. For a single junction in the stack, we observe the splitting of the flux-flow mode into M modes, each of them being characterized by different magnetic field dependence and by different cavity-resonance (Fiske-mode) frequency. Our results suggest that a fluxon moving in one junction in the stack may experience M=N different Swihart velocities due to the coupling to adjacent junction(s) through the common electrode(s) of the thickness smaller than the London penetration depth. In the twofold stacks, we find an indication for a coherent mode corresponding to coupled fluxon arrays moving in both junctions.

We have observed pronounced interactions between two closely spaced microbridge Josephson junctions. Major effects are locking of the two critical currents to a single value and the synchronization of the voltages across the two bridges to the same value.

We study a simple theoretical model of the proximity effect between superposed normal and superconducting metal films. We imagine a potential barrier between the films and treat electron transmission through the barrier as a tunneling process. For thin films the model is soluble, and we can treat the BCS potential self-consistently and calculate the excitation spectrum. We compute the transition temperature, the energy gap, and the electronic density of states for comparison with tunneling experiments.

The similarity between the nature of tunneling supercurrents and
normal'' supercurrents is established theoretically, and experimental results are
discussed. It is shown that many varied types of behavior of barriers between
superconductors can be predicted on the basis of a few simple equations based on
straightforward assumptions. These equations can be justified by the microscopic
theory. (T.F.H.)

Three-terminal double-junction Nb/Al-AlOx-Nb/Al-AlOx-Nb tunnel devices with a thin (≈ 13 nm) Nb/Al middle layer have been investigated. Strong interaction between the two junctions has been observed, as a result at zero voltage the system can behave like a single junction with one critical current. This state is stable and can be characterized by identical phase distributions for the two junctions. At some value of the applied magnetic field, a transition to another state occurs, in which the individual junctions behave relatively independently.

Using a whole-wafer route, the authors have fabricated
high-quality three-terminal Nb(AlO<sub>x</sub>)Nb(AlO<sub>x</sub>)Nb
devices with lead connections to each of the Nb layers, the middle Nb
layer being on the order of 10 nm thick. A detailed description is
presented of the adopted processing route, and recent results showing
the junctions, independently biased, behaving as strongly coupled
oscillators are discussed. The characteristics of the individual
junctions show that the additional processing required to make the
middle connection does not reduce the quality of the junctions.
Preliminary results also show that the close proximity of the junctions
possible with this route ensures strong inductive coupling (calculations
for the present wafer dimensions give a coupling coefficient of 0.6)
indicating its potential application in millimeter-wave coupling

A method is described for observing the proximity effect in a thin-film-superconductor-normal-metal bilayer. The superconducting film must be thin compared to its penetration depth. The kinetic inductance of the superconducting film alone is then proportional to lambda2(T)/d. It is found that in a bilayer the temperature dependence of the kinetic inductance deviates significantly from this dependence at low temperatures. The kinetic inductance may be measured in a nondestructive manner using the two-coil mutual-inductance technique. Bilayers of NbN/Al and Nb/Cu have both exhibited the effect, whereas a bilayer in which the proximity coupling was purposefully suppressed had the same temperature dependence as the superconducting film alone. The effect is analyzed in terms of a spatially varying penetration depth through the film thickness, and the observations are found to be in qualitative agreement with the predictions of the model. A more exact fitting will require improved theoretical models for the proximity effect.

It was recently suggested that coupling between the superconducting Cu-O bilayer or trilayer units in the highly anisotropic, high-temperature superconductors (HAHTS) can be described by incoherent Josephson tunneling. This paper confirms the assumed inverse dependence of the coupling energy on field, {ital H}, through measurements of the zero-bias resistance of discrete, high-quality, thin-film Nb Josephson junctions. This 1/{ital H} dependence was used to explain the flux-motion-induced broadening of resistive transitions in HAHTS for the equivalent geometry with {ital H} parallel to the {ital c} axis. The Nb junction results also unambiguously confirm another recent suggestion: that field-induced dissipation can occur in Josephson junctions without the motion of vortices from an externally applied field, which in this case are pinned in the Nb electrodes.

We have investigated the coupling between CuO2 layers in high-Tc superconductors by direct measurements of all dc and ac Josephson effects with current flow in the c-axis direction. The measurements have been performed on small single crystals of Bi2Sr2CaCu2O8, (PbyBi1-y)2Sr2CaCu2O8, Tl2Ba2Ca2Cu3O10, and YBa2Cu3O7-x and on a-axis-oriented YBa2Cu2O7 thin films. The results clearly show that all materials behave like stacks of superconductor-insulator-superconductor Josephson junctions. The current-voltage characteristics exhibit large hystereses and multiple branches, which can be explained by a series connection of highly capacitive junctions. From the modulation of the critical current in a magnetic field parallel to the layers, we infer a junction thickness of approximately 15 Å. In our microwave emission experiments we were able to prove explicitly that every pair of CuO2 double or triple layers forms a working Josephson contact. An exception is YBa2Cu3O7, where only flux-flow behavior has been observed.

- S Sakai
- P Bodin
- N F Pedersen

[II
121
[31
[41
[51
[61
[71
[81
[91
S. Sakai, P. Bodin and N.F. Pedersen, J. Appl. Phys. 73
(1993) 241 I.

- A V Ustinov
- H Kohlstedt
- M Clrillo
- N F Pedersen
- G Hallmanns
- C Heiden

A.V. Ustinov, H. Kohlstedt, M. Clrillo, N.F. Pedersen, G.
Hallmanns and C. Heiden, Phys. Rev. B 48 (1993) 10614.

- I P Nevirkovets
- J E Evetts
- M G Blamirc

I.P. Nevirkovets, J.E. Evetts and M.G. Blamirc, Phys. Lett. A
187 (1994) 119.

- R Kleiner
- P Mueller

R. Kleiner and P. Mueller, Phys. Rev. B 49 ( 1994) 1327.

- D H Kim
- K E Gray
- J H Kane

D.H. Kim, K.E. Gray and J.H. Kane. Phys. Rev. B 45 (1992)
7563.

Dynamics of Josephwn junctions and cllwtllts (Gordon and Breach

- K K Likharev

K.K. Likharev. Dynamics of Josephwn junctions and cllwtllts
(Gordon and Breach, New York. 1986)