Commensurability effects in a Josephson tunnel junction in the field of an array of magnetic particles

Commensurability effects have been theoretically studied in a hybrid system consisting of a Josephson junction located in a nonuniform field induced by an array of magnetic particles. A periodic phase-difference distribution in the junction that is caused by the formation of a regular lattice of Abrikosov vortices generated by the magnetic field of the particles in superconducting electrodes is calculated. The dependence of the critical current through the junction I _c on the applied magnetic field H is shown to differ strongly from the conventional Fraunhofer diffraction pattern because of the periodic modulation of the Josephson phase difference created by the vortices. More specifically, the I _c(H) pattern contains additional resonance peaks, whose positions and heights depend on the parameters and magnetic state of the particles in the array. These specific features of the I _c(H) dependence are observed when the period of the Josephson current modulation by the field of the magnetic particles and the characteristic scale of the change in the phase difference by the applied magnetic field are commensurable. The conditions that determine the positions of the commensurability peaks are obtained, and they are found to agree well with experimental results.     

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.     

Whole-wafer fabrication process for three-terminal double stacked tunnel junctions

A new fabrication process for three-terminal superconducting devices consisting of two Josephson junctions in a stacked configuration is reported. The process is based on the deposition of the whole Nb/Al_xO_y/Nb-Al/Al_xO_y/Nb multilayer on a Si crystalline wafer without any vacuum breaking. Lift-off techniques, anodization processes and a SiO film deposition have been adopted for patterning and insulating the two tunnel stacked junctions. Devices have been characterized in terms of current-voltage (I-V) curves and Josephson critical current vs. the externally applied magnetic field. They show high quality factors (V _m values up to 65 mV at 4.2 K), and good current uniformity. Received 5 June 2001     

Anomalous proximity effect in superconducting oxide structures with an antiferromagnetic layer

The electrophysical parameters of superconductor/antiferromagnetic insulator structures based on the Nb/Au/Ca_1?x Sr _x CuO₂/YBa₂Cu₃O_7?δ hybrid heterostructure have been examined. YBa₂Cu₃O_7?δ and Ca_1?x Sr _x SuO₂ epitaxial films are grown by the laser ablation method on NdGaO₃ single crystal substrates, the thickness of the Ca_1?x Sr _x CuO₂ layer varies from 20 to 50 nm, and x = 0.15 and 0.5. The superconducting pair potential in the interface between the YBa₂Cu₃O_7?δ superconductor and Ca_1?x Sr _x CuO₂ antiferromagnet is found to penetrate into the antiferromagnet at distances much larger than the coherence length calculated for the ferromagnetic layer. The critical current of the superconducting transition manufactured at such an interface is highly sensitive to the magnetic field.     

Realization of a Double-Slit SQUID Geometry by Fermi Arc Surface States in a WTe<Subscript>2</Subscript> Weyl Semimetal

We experimentally study electron transport between two superconducting indium leads, coupled to the WTe₂ crystal surface. WTe₂ is characterized by presence of Fermi arc surface states, as a predicted type-II Weyl semimetal candidate. We demonstrate Josephson current in unprecedentedly long 5 µm In–WTe₂–In junctions, which is confirmed by I–V curves evolution with temperature and magnetic field. The Josephson current is mostly carried by the topological surface states, which we demonstrate in a double-slit superconducting quantum interference device geometry, realized by coupling the opposite WTe₂ crystal surfaces.     

Influence of nonuniform critical current density profile on magnetic field behavior of AC susceptibility in 2D Josephson junction arrays

Employing mutual-inductance measurements, we study the magnetic field dependence of complex AC susceptibility of artificially prepared highly ordered (periodic) two-dimensional Josephson junction arrays of unshunted Nb-AlO_x-Nb junctions. The observed behavior can be explained assuming single-plaquette approximation of the overdamped model with an inhomogeneous critical current distribution within a single junction.     

Dependence of the maximal superconducting current on the resonance frequency in a shunted Josephson junction

We have analyzed the phase dynamics and current–voltage characteristics of a Josephson junction shunted by an LC circuit. When the Josephson frequency ω _J becomes equal to the natural frequency ω_rc of the formed resonance circuit, the I–V curve acquires additional branches. We have studied the features of the rc branch and the superconducting circuit for different values of the resonance frequency. It is shown that the maximal superconducting current through the Josephson junction on the rc-branch depends on the resonance frequency and is determined by the closeness of the end point of the rc branch to the critical current. We have determined the dependence of the maximal superconducting current on the resonance frequency for different values of the dissipation parameters. The limiting value of the maximal superconducting current is independent (to within 1%) of the parameters of the system.     

Superconducting vortex line in Josephson junction

The superconducting ring closed with the half infinite plane Josephson junction is considered. The external magnetic flux is introduced in the ring with the external source supplied solenoid.The conditions of stability are found for the superconducting vortex in the plane Josephson junction. The function φ(φ_x) is derived. Here φ is the total magnetic flux in the hole. This function differentiates from the same function in the case of the ring closed. with the point contact.     

Investigation of the Josephson coupling through a magnetoactive barrier (ferrimagnet, paramagnet) in Y3/4Lu1/4Ba2Cu3O7 + Y3(Al1 − x Fe x )5O12 composites

The transport properties of two-phase composites consisting of a high-temperature superconductor and a nonsuperconducting component with magnetic ordering are analyzed. These composites are considered as a network of “superconductor-magnetoactive insulator-superconductor” weak links of the Josephson type. Substituted garnets Y₃(Al_{1 ? x} Fe _x )₅O₁₂ (x = 0, ..., 1.0) are used as a magnetoactive component. The composites under investigation contain 92.5 vol % Y_3/4Lu_1/4Ba₂Cu₃O₇ (the high-temperature superconductor) and 7.5 vol % Y₃(Al_{1 ? x} Fe _x )₅O₁₂ (x = 0, ..., 1.0). It is shown that an increase in the iron content in the Y₃(Al_{1 ? x} Fe _x )₅O₁₂ garnet leads to a reduction of the Josephson coupling strength: the temperature range in which the electrical resistance of the composites is equal to zero is reduced, and the critical current density at a temperature of 4.2 K decreases exponentially. For composites in which the iron content in the Y₃(Al_{1 ? x} Fe _x )₅O₁₂ garnet is higher than 0.1, the temperature dependence of the electrical resistance R(T) at temperatures below the transition point T _C of high-temperature superconductor crystallites has a portion in the range T _m -T _C where the resistance R(T) is independent of the transport current and the magnetic field strength. Below the temperature T _m , the dependences of the electrical resistance R(T) of the composites are nonlinear functions of the current and involve a considerable contribution from magnetoresistance. This behavior is characteristic of a network of Josephson junctions. The temperature T _m decreases with an increase in the iron content in the Y₃(Al_{1 ? x} Fe _x )₅O₁₂ garnet. The appearance of the above feature in the temperature dependences of the electrical resistance R(T) is interpreted as complete suppression of the Josephson coupling in the temperature range above T _m due to the interaction of supercurrent carrier pairs with magnetic moments of iron atoms in the dielectric barriers separating high-temperature superconductor grains.     

Mechanisms of dissipation in a Josephson medium based on a high-temperature superconductor in a magnetic field

This paper reports on the results of an investigation into the influence of magnetic fields (0–60 kOe) on the temperature dependences of the electrical resistance R(T) of the Y_3/4Lu_1/4Ba₂Cu₃O₇ + CuO composites. The structure of these composites is considered to be a network of tunnel-type Josephson junctions in which a nonsuperconducting component (CuO) forms boundaries (barriers) between high-temperature superconducting crystallites. The temperature dependence R(T) of the composites has two steps characteristic of granular superconductors: (i) an abrupt change in the electrical resistance at the critical temperature of high-temperature superconducting crystallites and (ii) a smooth transition to the superconducting state under the influence of the boundaries between the crystallites. The experimental dependences R(T) are analyzed within the Ambegaokar-Halperin model of thermal fluctuations in Josephson junctions and the flux creep model. An increase in the magnetic field leads to a crossover from the Ambegaokar-Halperin mechanism to the flux creep mechanism. The temperature dependences R(T) in the range of weak magnetic fields (from 0 to 10² Oe) are adequately described by the relationship following from the Ambegaokar-Halperin model. In the range of strong magnetic fields (from 10³ to 6 × 10⁴ Oe), the dissipation obeys the Arrhenius law R ～ exp(?U(H)/T)], which is characteristic of the flux creep model with a temperature-independent pinning energy U(H). The effective Josephson coupling energies and the pinning energies corresponding to the Ambegaokar-Halperin and flux creep mechanisms are determined.     

Locally frozen magnetic field in HTSC ceramics

The value of a locally frozen magnetic field in a region with a diameter of 0.5 mm in a 0.5-mm-thick YBa₂Cu₃O_{7 ? x} plate was investigated as a function of the excitation field (to 2 × 10⁴ Am^?1), plate cooling mode (in the absence or presence of a field; i.e., zero-field cooling (ZFC) or field coupling (FC)), and local demagnetizing field. Analysis of the measurement results in the noted range of excitation fields showed the following: (i) the dependence on the excitation field for the ZFC mode is explained by the local inhomogeneity of critical currents of weak links in the ceramic Josephson medium and is limited by their maximum value at the temperature of the experiment (77 K); (ii) the dependence on the excitation field for the FC mode contains a portion of the magnetic phase transition from the frozen current structure, typical of the initial portion of the dependence, to the current structure characteristic of the ZFC freezing mode, and is limited by this transition; and (iii) the dependence on the demagnetizing field for the ZFC mode can be explained by the stable coexistence (without annihilation) of microscopic current loops with opposite current directions in the ceramics.     

Enhancement of superconductivity by an external magnetic field in magnetic alloys

An infinite-volume limit solution of the thermodynamics of a BCS superconductor containing spin 1/2 and 7/2 magnetic impurities, obtained recently in [D. Borycki, J. Ma?kowiak, Supercond. Sci. Technol. 24, 035007 (2011)] is exploited to derive the expressions for critical magnetic field $\mathcal{H}_c$ (T). The credibility of the resulting thermodynamically limited theoretical equations, which depend on the magnetic coupling constant g and impurity concentration c, is verified on the experimental data for the following superconducting alloys: LaCe, ThGd and SmRh₄B₄. Good quantitative agreement with experimental data is found for sufficiently small values of c. The discrepancies between theoretical and experimental values of $\mathcal{H}_c$ (T) for larger values of c in case of LaCe and ThGd are reduced by introducing the concept of the effective temperature $\tilde T$ , which accounts for the Coulomb interactions between the electron gas and impurity ions. At low temperatures, the critical magnetic field is found to increase with decreasing temperature T. This enhancement of the critical magnetic field provides evidence of the Jaccarino-Peter effect, which was experimentally observed in the Kondo systems like LaCe, (La_{1 ? x} Ce _x )Al₂ and also in the pseudoternary compounds, including Sn_{1 ? x} Eu _x Mo₆S₈, Pb_{1 ? x} Eu _x Mo₆S₈ and La_{1.2 ? x} Eu _x Mo₆S₈. The effect of an external magnetic field $\mathcal{H}$ on a BCS superconductor perturbed by magnetic impurities was also studied. On these grounds, by analyzing the dependence of superconducting transition temperature T _c on $\mathcal{H}$ of (La_{1 ? x} Ce _x )Al₂, we have shown, that for certain parameter values, external magnetic field compensates the destructive effect of magnetic impurities.     

Magnetoresistance of superconducting grains in ceramic YBa2Cu3O7 − δ high-temperature superconductors in weak magnetic fields

The current-voltage characteristics $E(j)_{H_{treat} } = const$ of ceramic (granular) YBa₂Cu₃O_6.95 samples preliminarily magnetized in different transverse magnetic fields H _treat have been measured in a zero field (H _ext = 0) at T = 77.3 K for elucidating specific features of dissipation in superconducting grains of high-temperature superconductors (HTSCs). The current-voltage curves measured in the range 0 ≤ H _trap ≤ H _c2J (where H _trap is the magnetic field trapped as a result of the pretreatment in H _treat and H _c2J is the upper critical field of the Josephson weak links) have been used to construct the field dependences of the magnetoresistance ρ_A(H _treat) _{j = const} of superconducting grains. It has been established that the magnetoresistance ρ_A of the superconducting grains is significantly lower than the magnetoresistance ρ_J for the Josephson medium. The dependence of ρ_A on H _treat and on the transport current density j has been investigated. It has been shown that the dependences ρ_A(H _treat) _{j = const} exhibit a clearly pronounced tendency to saturation, ρ_satur, and the value of ρ_satur increases with increasing j. It has been found that the lower critical field H _c1A of the superconducting grains strongly depends on the transport current density.     

Josephson effects in long superconducting bridges with variable thickness

We have studied the properties of long (L≈20μm) superconducting threads (Pb or Sn) formed by pulse electrical breakdown in monocrystalline silicon. These long bridges with variable thickness have well defined d.c. and a.c. Josephson effects in large temperature range (T/T_c?0.2 and 0.4 for Pb and Sn, respectively) and high magnetic fields (up to 0.14T for Pb at 4.2 K). In the whole temperature range, the critical current has linear temperature dependence, as for “ideal” Josephson junctions. The results are interpreted by coherent motion of vortices. Some interesting results about satellites of quasiparticle gap structures and the asymmetry of these structures with respect to the current direction are presented.     

Specific features of magnetic field penetration into granular superconductors and possible sensitivity of magnetic sensors based on them

The results of experimental and theoretical studies of the magnetic properties of a superconducting ceramic with the composition YBa₂Cu₃O_{7 ? x} are presented. The limiting sensitivity of magnetic field sensors on the basis of a high-temperature superconducting ceramic is discussed.     

Effect of the characteristics of a superconductor on the levitation properties of the magnet-superconductor system

The results of the experimental and theoretical investigations of the magnetic levitation force appearing at the interaction of the multilayer superconducting block of the YBa₂Cu₃O_7?x melted textured ceramic and a permanent magnet are presented. The maximum repulsive force and maximum attractive force are determined as functions of the thickness of the superconducting block in the superconductor cooling regime in both zero and nonzero magnetic fields. The dependence of the levitation force on the geometric parameters and critical current of the superconductor is found.     

Critical current of a textured granular superconductor in high magnetic fields

The critical current density J _c is studied theoretically using the cluster model of a granular superconducting structure for the case where Abrikosov vortices are present in the grains. It is found that the dependence of J _c on the effective ratio of the sizes of grains forming an intergrain Josephson junction is Gaussian. The dependence of J _c on the anisotropy of the penetration of a magnetic field into the grains is shown to reduce to the dependence on the coupling strength between the crystallites.     

Maximal supercurrent of a Josephson junction in a field of magnetic particles

The maximal supercurrent I_m of a short Josephson junction formed by an edge contact of two superconducting films is calculated for the case where the junction is placed in a periodic field produced by a chain of magnetic nanoparticles. The commensurability effects occurring when the magnetic flux of a homogeneous external field H₀ through an elementary cell is equal to an integral number of magnetic flux quanta Φ₀ are considered. The effects give rise to additional maxima in the I_m(H₀) dependence.     

Andreev states and the Josephson effect in superconducting heterojunctions on thin YBa2Cu3Ox films

Conductance anomalies at low bias voltages and superconducting currents in Au/YBa₂Cu₃O_x and Nb/Au/YBa₂Cu₃O_x heterojunctions in which the c axis of the YBa₂Cu₃O_x (YBCO) epitaxial film is rotated in the (110) YBCO plane through 11° with respect to the normal to the substrate plane were studied experimentally. The films were prepared by laser deposition onto (7 2 10)-oriented NdGaO₃ substrates. The current-voltage characteristics of the heterojunctions exhibit conductance anomalies at low voltages. The behavior of these anomalies is studied at various temperatures and in various magnetic fields. The critical current and Shapiro steps observed in the current-voltage characteristics of Nb/Au/YBa₂Cu₃O_x were evidence of the Josephson effect in these heterojunctions. The experimental results are analyzed in terms of the model of the arising of bound states caused by Andreev reflection in superconductors with d-type symmetry of the superconducting order parameter.     

Magnetic phase transition in ɛ-In x Fe2 − x O3 nanowires

This paper reports on a study of magnetic properties of ordered arrays of ?-In _x Fe_{2 ? x} O₃ (x = 0.24) nanowires possessing a high room-temperature coercive force of 6 kOe. Lowering the temperature below 190 K brings about a sharp decrease of the coercive force and magnetization of nanowires driven by the magnetic phase transition from the ferrimagnetic into antiferromagnetic phase. The transition is accompanied by a decrease of the magnetic anisotropy constant, which accounts for the anomalous frequency dependence of the position of the maximum in the temperature dependence of dynamic magnetic susceptibility. In the low-temperature phase, a spin-flop transition in the magnetic field of 28 kOe has been observed at T = 2 K. Lines related to the high-temperature hard-magnetic and low-temperature phases have been identified in electron spin resonance spectra of the nanowires. A line lying near zero magnetic field and evolving from the nonresonant signal related to the microwave magnetoresistance of the sample has also been detected.