Josephson (001) tilt grain boundary junctions of high-temperature superconductors

We calculate the Josephson critical current I_c across in-plane (001) tilt grain boundary junctions of high-temperature superconductors. We solve for the electronic states corresponding to the electron-doped cuprates, two slightly different hole-doped cuprates, and an extremely underdoped hole-doped cuprate in each half-space, and weakly connect the two half-spaces by either specular or random Josephson tunnelling. We treat symmetric, straight, and fully asymmetric junctions with s-, extended-s, or d _{x ²?y ²} -wave order parameters. For symmetric junctions with random grain boundary tunnelling, our results are generally in agreement with the Sigrist–Rice form for ideal junctions that has been used to interpret ‘phase-sensitive’ experiments consisting of such in-plane grain boundary junctions. For specular grain boundary tunnelling across symmetric junctions, our results depend upon the Fermi surface topology, but are usually rather consistent with the random facet model of Tsuei et al. Our results for asymmetric junctions of electron-doped cuprates are in agreement with the Sigrist–Rice form. However, our results for asymmetric junctions of hole-doped cuprates show that the details of the Fermi surface topology and of the tunnelling processes are both very important, so that the ‘phase-sensitive’ experiments based upon in-plane Josephson junctions are less definitive than has generally been thought.     

Investigation of step-edge Josephson device of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−<Emphasis Type="Italic">d</Emphasis></Subscript> formed on MgO by a pulsed laser deposition method

We fabricated step-edge Josephson junctions of YBa₂Cu₃O_7−d on MgO substrates by a pulsed laser deposition method for high frequency applications. On the basis of temperature dependence of critical current, noticeable deterioration has not been observed in a step-edge area. The dynamic resistance was between 2 and 3Ω under the superconducting critical temperature. A deviation from a resistively shunted junction model was observed, which implies the excess current not flowing through Josephson junctions.     

Ac-Josephson effect in YBa2Cu3O7/PbSn point contact junctions

Adjustable YBa₂Cu₃O₇/PbSn point contact Josephson junctions are exposed to a microwave field. The current voltage characteristics of the junctions show microwave-induced constant voltage steps. The power dependence of the current width of the steps is well described by the Bessel function behaviour. This clearly demonstrates the presence of macroscopic quantum effects in the new highT _c material.     

Current-phase relation in SFS Josephson junctions in the presence of <Emphasis Type="Italic">s</Emphasis>-<Emphasis Type="Italic">d</Emphasis> scattering

The analytical equations for the current-phase relation (CPR) coefficients for Josephson junctions with a ferromagnetic interlayer in the model where the scattering from s- to d-band is considered to be the main type scattering of charge carrier in a ferromagnet are obtained. It is shown that the magnitude of the coefficients oscillates and decays with an increase of the interlayer thickness. Both the oscillation period and the decay length for the first and the second harmonics differ by two times. The temperature dependence of the critical current demonstrating 0-π temperature transitions is obtained. The possibility of design a flux qubit based on such Josephson junctions is demonstrated.     

Ferromagnetic 0–<Emphasis Type="BoldItalic">π</Emphasis> Josephson junctions

We present a study on low-T_c superconductor-insulator-ferromagnet-superconductor (SIFS) Josephson junctions. SIFS junctions have gained considerable interest in recent years because they show a number of interesting properties for future classical and quantum computing devices. We optimized the fabrication process of these junctions to achieve a homogeneous current transport, ending up with high-quality samples. Depending on the thickness of the ferromagnetic layer and on temperature, the SIFS junctions are in the ground state with a phase drop of either 0 or π. By using a ferromagnetic layer with variable step-like thickness along the junction, we obtained a so-called 0–π Josephson junction, in which 0 and π ground states compete with each other. At a certain temperature the 0 and π parts of the junction are perfectly symmetric, i.e. the absolute critical current densities are equal. In this case the degenerate ground state corresponds to a vortex of supercurrent circulating clock- or counterclockwise and creating a magnetic flux which carries a fraction of the magnetic flux quantum Φ₀. PACS  74.50.+r; 74.78.Fk; 74.81.-g; 85.25.Cp     

Breathing charge density waves in intrinsic Josephson junctions

We demonstrate the creation of a charge density wave (CDW) along a stack of coupled Josephson junctions (JJs) in layered superconductors. Electric charge in each superconducting layer oscillates around some average value, forming a breathing CDW. We show the transformation of a longitudinal plasma wave to CDW in the state corresponding to the outermost branch. Transition between different types of CDW’s related to the inner branches of IV characteristic is demonstrated. The effect of the external electromagnetic radiation on the states corresponding to the inner branches differs crucially from the case of the single JJ. The Shapiro steps in the IV characteristics of the junctions in the stack do not correspond directly to the frequency of radiation ω. The system of JJs behaves like a single whole system: the Shapiro steps or their harmonics in the total IV characteristics appear at voltage $\sum {V_l } = N_R \frac{m} {n}\omega$ , where V _l is the voltage in the lth junction, N _R is the number of JJs in the rotating state, and m and n are integers.     

High-T c Josephson junctions for electronic applications

Summary The current status of the electronic applications of high-T _c Josephson junctions is briefly reviewed. Recent results obtained by the authors on devices employing step-edge junctions are reported. In particular the design of a microwave oscillator based on a parallel array of junctions is discussed and preliminary experimental results are presented. Paper presented at the ?VII Congresso SATT? Torino, 4–7 October 1994.     

Static characteristics of Josephson interferometers

This investigation deals with the range in operating currents for which a Josephson interferometer, sometimes also referred to as Superconducting QUantum Interference Device (SQUID), may remain in the zero-voltage Josephson condition. An interferometer consists of one or more inductive loops each of which contains two Josephson junctions or other weak links. Two types of current are considered. Gate currentI _gpasses the junctions in parallel. Control currentI _cgenerates magnetic flux via inductive coupling in the loops. Zero-voltage operation is possible within certain areas of theI _g,I _cplane. These areas are manifestations of flux-quantum states and their boundary lines are referred to as static characteristics. In view of the nonlinearity of the constituting equations, not all their formal solutions are physically realizable. A stability analysis yields criteria which permit the identification of realizable operating conditions. The static characteristics comprise operating conditions where the limit of stability is reached. To obtain the static characteristics, linearized equations may be utilized if theLI _o product, a measure for the size of an interferometer, is large compared to the flux quantumΦ ₀, whereL is the inductance per loop, andI _o the maximum Josephson current per junction. As a general method of solving system of transcendental equations, continuation is discussed. The utilization of continuation for obtaining interferometer characteristics is explained. It is shown that some changes in the gate-current feed arrangement are equivalent to shearing the characteristics in theI _g,I _cplane. Analytical results are given on extrema, inflexion points, and singularities in the shape of cusps which conceptually relate to the existence and connectivity of flux-quantum states. Experimental static characteristics are presented on two-and four-junction interferometers. They are in agreement with characteristics computed on the basis of simple lumped circuit models. Relevant circuit parameters are obtained from the experimental characteristics.     

The Relation Between Barrier Structure and Current Uniformity in YBCO Josephson Junctions

Electromagnetic transport measurements were combined with high-resolution electron microscopy observations to study the relation between structure and local critical currents in YBa₂Cu₃O_7–x (YBCO) Josephson junctions. The spatial variation of the critical current J(x) along the length of the boundary for interface engineered Josephson junctions and bicrystal grain boundary Josephson junctions was determined using a phase retrieval algorithm. The current distribution solutions were found to be highly uniform along the length of interface engineered junctions in contrast to solutions for grain boundary junctions. The latter showed significant spatial oscillations in the critical current as well as areas along the boundary that carried no current. Microstructural evaluation of interface engineered junctions fabricated using identical processing parameters to the junctions used for transport measurements suggest that the uniform current distribution is controlled by a highly uniform barrier layer formed between the superconducting electrodes. Microstructural evaluation of grain boundary junctions similar to the junctions used for transport measurements show considerable variations of the grain boundary structure within a single junction.     

Characteristics of the Surface-Intrinsic Josephson Junction

During the fabrication of intrinsic Josephson junctions (IJJs) with Bi₂Sr₂CaCu₂O_8+δ (BSCCO) single crystals, the superconductivity of the surface Cu-O layer is degraded because of a deposited metal film on top of the stack. Thus, the characteristics of the surface junction consisting of the surface Cu-O double layers remarkably differ from those of the junctions deep in the stack, which will be referred to as ordinary IJJs. The electrical transport characteristics of the surface junction, such as I-V, I _c′-T, and R-T, show that the critical temperature T _c′ of the surface junction is always lower than that of ordinary IJJs, and that the change of its critical current I _c′ with temperature is different from that of ordinary IIJs. Furthermore, by shunting the surface junction resistively, we are able to observe the AC Josephson effect at 3-mm waveband. Translated from Chinese Journal of Low Temperature Physics, 2005, 27(2) (in Chinese)     

Josephson effect through a ferromagnetic layer

We report transport measurements on Superconductor/Ferromagnet/Superconductor (S/F/S) junctions: Nb/Al/Gd/Al/Nb where gadolinium (Gd) is a weakly polarized ferromagnet. A sizeable critical current I _c is observed in the I(V) characteristics. This current can be modulated by a weak magnetic field, as expected for a Josephson current. With these experiments, we establish that superconducting coherent transport survives across a small ferromagnetic layer. The penetration depth of Cooper pairs in Gd has been measured. An extensive study of the Josephson critical current in temperature for different thicknesses of magnetic compounds is presented. A comparison of transport measurements with S/N/S junction is given through measurements made on Nb/Al/Y/Al/Nb, where yttrium (Y) is used as non magnetic rare earth metal. Received 20 September 2000 and Received in final form 22 February 2001     

Double resonance in the system of coupled Josephson junctions

The effect of LC shunting on the phase dynamics of coupled Josephson junctions has been examined. It has been shown that additional (rc) branches appear in the current-voltage characteristics of the junctions when the Josephson frequency ω_J is equal to the natural frequency of the formed resonance circuit ω_rc. The effect of the parameters of the system on its characteristics has been studied. Double resonance has been revealed in the system at ω_J = ω_rc = 2ω_LPW, where ω_LPW is the frequency of a longitudinal plasma wave appearing under the parametric-resonance conditions. In this case, electric charge appears in superconducting layers in the interval of the bias current corresponding to the rc branch. The charge magnitude is determined by the accuracy with which the double resonance condition is satisfied. The possibility of the experimental implementation of the effects under study has been estimated.     

Planar graphene Josephson coupling via van der Waals superconducting contacts

We report on the fabrication and transport characteristics of van der Waals (vdW)-contacted planar Josephson junctions. In a device, two pieces of cleaved 2H-NbSe₂ superconducting flakes and a monolayer graphene sheet serve as the superconducting electrodes and the normal-conducting spacer, respectively. A stack of NbSe₂?graphene?hexagonal-boron-nitride (hBN) heterostructure with clean and flat interfaces was prepared by a dry transfer technique. The outermost hBN layer protected the NbSe₂?graphene?NbSe₂ Josephson junction from chemical contamination during the fabrication processes. The Josephson coupling was confirmed by a periodic modulation of the junction critical current $I_{\text{c}}$ in a perpendicular magnetic field. The temperature dependence of $I_{\text{c}}$ showed long and diffusive Josephson coupling characteristics. The temperature dependence of the superconducting gap, obtained from the multiple Andreev reflection features, followed the Bardeen?Cooper?Schrieffer (BCS) prediction.     

Intrinsic Josephson tunneling for basic studies of high-temperature superconductors

High-temperature superconductors (HTS) are highly anisotropic with layers of CuO₂ separated by layers of charge reservoirs. The superconducting CuO₂ planes are weakly coupled by Josephson tunneling of Cooper pairs in the c-axis direction. It may be possible to use the intrinsic tunneling to realize a stack of intrinsic Josephson junctions at the surface of a single crystal (or epitaxial film) of HTS. These will form excellent tools in the study of superconducting properties of HTS.     

Subharmonic Shapiro steps and noise in high-T c superconductor Josephson junctions

An experimental investigation is made of the subharmonic Shapiro steps observed on the I-V curves of high-T _c superconductor Josephson junctions and on the bias-voltage dependences of the rf noise and detector response when the junctions are subjected to external submillimeter radiation. Structures of this type are ordinarily described by a nonsinusoidal current-phase relation, which is why subharmonic steps appear. Numerical modeling of the processes occurring in a Josephson junction by means of a simple current-phase relation, as in the case of an SNS junction, gives good agreement with experiment. The width of the characteristic Josephson generation line of the junction was estimated on the basis of the noise dependences and the selective detector response. The width can be explained by taking into account the shot noise of the tunneling component of the conductivity. A model of the conductivity of a high-T _c superconductor Josephson junction, consisting of a tunnel junction with microshorts possessing metallic conductivity, is discussed. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 5, 426–430 (10 September 1998)     

Proximity-induced transport in hybrid mesoscopic normal–superconducting metal structures

Using an approach based on quasiclassical Green’s functions we present a theoretical study of transport in mesoscopic SN structures in the diffusive limit. The subgap conductance in SN structures with barriers (zero bias and finite bias anomalies) are discussed. We also analyse the temperature dependence of the conductance variationδS (T) for a Andreev interferometer. We show that besides the well know low temperature maximum a second maximum near T_cmay appear. We present the results of studies on the Josephson effect in 4-terminal SNS contacts and on the possible sign reversal of the Josephson critical current.     

Synchronisationseffekte in einer linearen Anordnung aus N Josephson-Verbindungen

Synchronization Effects in a Linear Array of N Josephson Junctions Within the frame of the RSJ model we investigate the synchronization of the oscillations in a linear array of N identical Josephson junctions shunted by an electromagnetic resonator. Using an adiabatic approximation to the first order of the parameter I_cI the reduced equations of the slowly varying phases are derived. These equations allow the detailed investigation of all the stationary states of the system. Only the coherent state in the inductive regime and the radiationless state in the capacitive regime are found to be stable. Including noise effects we discuss the order parameter concept for the resonator current in the case N ? 1.     

The role of the surface depression of the pair potential on the Josephson and quasi-particle tunnelling in high-T c superconductors

Summary We discuss the influence of the intrinsic surface depression of the order parameter on the temperature dependence of the Josephson critical currentI _c(T) and, tentatively, on the quasi-particle tunnelling conductance in a superconductor with a very short coherence length. The comparison with the experiments shows that the presence of a surface-depressed pair potential can explain the large deviations of theI _c(T) from the ideal BCS behaviour that we recently observed in Bi₂Sr₂CaCu₂O_8+x Josephson break junctions and could mimic the presence of a broadening in the Superconductor-Insulator-Normal tunnelling conductance of the same high-T _c superconductor. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

Nanosize patterns as reference structures for macroscopic transport properties and vortex phases in YBCO films

This paper reports on the striking correlation between nanosize mosaic domain walls in YBCO films and 1D rows of parallel Josephson junctions, determining the J _c vs.B curves. From X-ray data analysis, it results that the average “hidden" domain wall, faceted at a nanometric scale, is almost mimicking the Josephson Junction (JJ) 1D array. The assumption that the JJs and the domain-wall arrays are coincident, enables to find out the particular scaling field, making the J _c vs.B curves independent of temperature. This scaling field can be interpreted in terms of the Josephson nature of the transport current across these particular patterns in the intermediate temperature range. By means of our model it is also possible to calculate two asymptotic behaviors of the pinning force as a function of field, for low and high fields, respectively. These behaviors are punctually repeated by the experimental results in the same asymptotic limit, so that two corresponding vortex regimes are clearly pointed out. All results can be interpreted by concluding that in the intermediate temperature range, the strong pinning observed in high quality YBCO films is due to the Josephson Junctions average patterns. These patterns are the counterpart related to the transport mechanisms of “hidden" structural nano-domains. Received 16 October 2000 and Received in final form 28 November 2000     

Properties of YBa2Cu3O7−δ/YBa2CoxCu3−xOy/YBa2Cu3O7−δ Josephson edge junctions with 0.1 x 0.3 and the effect of flux flow on their normal resistance

YBa₂Cu₃O_7−δ (YBCO) based SNS edge junctions with cobalt doped YBCO barriers were prepared and characterized. At 77 K, good junctions had RSJ-like I–V curves with excess current, magnetic suppression of I_c of about 50% or more, and clear microwave steps. The conductance values 1/R_N at 77 K of junctions with different barrier thickness and composition, were proportional to the junction areas A, but show little correlation with the thickness of the barriers t_B in the range of 15t_B100nm. The corresponding I_cR_N products were observed to scale as J^0.66±0.09_c, similar to what was found by others. At the same time, the measured values of R_N are much smaller than what is expected based on the dimensions of the junction and the resistivity of the barrier material. To explain all of this, we propose a model in which at high supercurrent densities, flux flow of Josephson vortices in the junction leads to R_N values which are lower than expected. This model predicts

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, which fits the observed results very well.