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)     

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.     

Josephson and single-particle currents between partially dielectricized superconductors with charge-density waves

The amplitudes of the nonstationary Josephson current I ¹, the interference current I ², and the quasiparticle current J through symmetric and asymmetric tunnel junctions, including superconductors with charge density waves, are calculated. In the symmetric (s) case the dependence of the Josephson current I _s ¹ on the voltage V on the junction has a logarithmic singularity at |eV|=2Δ, Δ+D, and 2D, where , Δ and Σ are the superconducting and dielectric order parameters, and e is the unit charge. At temperatures T≠0 jumps appear in the current-voltage characteristics I _s ¹ (V) at |eV|=D−Δ. Jumps and singularities are observed in the currents I _s ² and J _s at the same voltages at which singularities and jumps appear in I _s ¹ , respectively. In the nonsymmetric (ns) junctions which include an ordinary superconductor, singularities and jumps occur at |eV|=D+Δ_BCS, Δ+Δ_BCS, and (for T≠0) |D−Δ_BCS| and |Δ−Δ_BCS|, where Δ_BCS is the order parameter of an ordinary superconductor. The quasiparticle current J _ns is an asymmetric function of the voltage V and does not depend on the sign of Σ. The results are compared with experiment. Fiz. Tverd. Tela (St. Petersburg) 39, 991–999 (June 1997)     

Weak-link bi-epitaxial Josephson junctions in a YBa2Cu3O7−δ film on BaZrO3/CeO2/SrTiO3

A bi-epitaxial (001)YBa₂Cu₃O_7−δ /(110)BaZrO₃/(001)CeO₂ three-layer heterostructure has been grown on (100)SrTiO₃ by laser ablation. The epitaxial relations between the layers making up the heterostructure were derived from x-ray diffraction data. The I _cR_n product for the bi-epitaxial Josephson junctions thus obtained was within 1–1.5 mV for 4.2 K, and 30–60 μV for 77 K. The normal resistance R _n=(2–5 Ω) was practically independent of temperature. The magnetic field dependences of I _c had typically a clearly pronounced main maximum, followed by distorted subsequent peaks. Interaction of the Josephson ac current with self-induced electromagnetic waves at the 45° grain boundary and with external microwave radiation (f=11 GHz) produced current steps in the I-V characteristics of the bi-epitaxial junctions at the corresponding voltages. Fiz. Tverd. Tela (St. Petersburg) 39, 1732–1738 (October 1997)     

Intrinsic tunneling study of underdoped Bi2Sr2-xLaxCuO6+δ superconductors

We report on a tunneling study of underdoped submicron Bi₂Sr_2-xLa_xCuO_6+δ (La-Bi2201) intrinsic Josephson junctions (IJJs), whose self-heating is sufficiently suppressed. The tunneling spectra are measured from 4.2 K up to the pseudogap opening temperature of T^* = 260 K. The gap value found from the spectral peak position is about 35 meV and has a weak temperature dependence both below and above the superconducting transition temperature of T_c = 29 K. Since the superconducting gap should have a value of 10-15 meV, our results indicate that the pseudogap (～35 meV) plays an important role in the underdoped La-Bi2201 intrinsic tunneling spectroscopy down to the lowest temperature of 4.2 K. However, the contribution of the superconducting gap can be separated by normalizing the spectra to the one near and above T_c, which shows that the IJJs can be a useful tool for the study of the electronic properties of the La-Bi2201 cuprate superconductors.     

SrTiO3基片上Tl-2212双晶约瑟夫森结的动态特性及噪声影响研究

在SrTiO₃（STO）基片上制作了Tl-2212双晶约瑟夫森结,并对其进行了微波辐照下的I-V特性测试,观察到了夏皮罗台阶,符合约瑟夫森电压-频率关系.利用数值仿真对约瑟夫森结建立了RCSJ模型,仿真结果与实验数据符合较好,利用此模型深入研究了噪声对结动态特性的影响,解释了噪声影响下结的微波感应台阶幅度减小和极小值展宽现象,提出了有效噪声温度为工作温度和外部噪声的等效温度之和. 关键词： RCSJ模型 噪声 Tl-2212双晶约瑟夫森结     

Chaotic dynamics of resistively coupled DC-driven distinct Josephson junctions and the effects of circuit parameters

Two distinct Josephson junctions (JJs) connected with a constant coupling resistance R_cp are theoretically considered to investigate the overall dynamics below and above the critical current I_c. The circuit model of the device is driven by two DC current sources, I₁ and I₂. Each junction is characterized by a nonlinear resistive–capacitive junction (NRCSJ). Having constructed the circuit model, time-dependent simulations are carried out for a variety of control parameter sets. Common techniques such as bifurcation diagrams, two-dimensional attractors and Lyapunov exponents are applied for the determination of chaotic as well as periodic dynamics of the superconducting junction devices. According to the findings, two states (namely superconducting and ordinary conducting) are determined as functions of the source currents. The chaotic current which flows through R_cp exhibits a very rich behavior depending on the source currents I₁ and I₂ and junction capacitances C₁ and C₂. The device characteristics are summarized by a number of three-dimensional phase diagrams in the parameter space. In addition, for certain parameters, hyper-chaotic cases with two positive Lyapunov exponents are encountered. In contrast to earlier studies claiming the need for a sinusoidal feeding current for generating a chaotic signal, our circuitry can easily generate one via a DC source.     

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.     

高温超导GdBa2Cu3O7-δ薄膜双晶晶界结特性研究

在晶界夹角为24°的YSZ人工双晶基片上,采用原位直流磁控溅射法制备了高温超导双晶GdBa₂Cu₃O_7-δ超导薄膜。采用光刻技术在晶界上刻出了尺寸5×5μm²的双晶晶界结。在77K下观测了结的直流I-V特性和在10GHz微波辐射下结的Shapiro台阶。这表明我们的人工双晶晶界结具有约瑟夫森弱连接行为。对结的特性进行了初步的理论分析和在实验基础上的数值模拟,模拟结果与RSJ理论符合较好,表明我们的双晶晶界结基本符合RSJ模型。     

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.     

Scanning tunneling spectroscopy of a superlattice superconductor: Bi2Sr2CaCu2O8

It is clear that many of the cuprate superconductors are truly superlattices, composed of sheets whose individual superconducting critical temperatures may approach bulk values. Such a cuprate is Bi₂Sr₂CaCu₂O₈, often referred to as BSCCO-2212. Scanning tunneling spectroscopy (vacuum tunneling) applied toa-bBiO cleavage planes ofT_c≈90 K BSCCO single crystals under liquid helium simultaneously provides topography and local dI/dVspectra (superconducting density of states: DOS). The spectra, which are similar to those obtained from angle-resolved photoemission spectroscopy, confirm a large gap parameter Δ(x,y) on the uppermost layer. The dI/dVspectra do not unequivocally select order parameter symmetry, but are probably consistent with d-wave or anisotropic s-wave states. Spatial variations of Δ on a 100 Å scale are attributed to variation in BiO metallicity, originating in oxygen stoichiometry variations. A model is presented to explain the different dI/dVspectra which are seen, and associated with different local oxygen concentrations. This model, based on the superconducting proximity effect, assumes that in some regions the BiO uppermost layer is insulating and in other regions it is metallic, in the latter case induced superconductivity by proximity to the CuO₂planes. Our STM measurements appear to sample only the uppermost half cell of the crystal, and contain no obvious superlattice features. Recent measurements have confirmed Josephson radiation from voltage biasedc-axis pillars of BSCCO. From the point of view of the present work, the superconducting systems which weakly couple along thec-direction to create Josephson junctions are probably half-cell slabs of height 15.4 Å, each containing two CuO₂and two BiO layers, which act as single composite electrodes for the Josephson junctions.     

Nonlinear Seebeck effect in a model granular superconductor

The change of the Josephson supercurrent density j _s of a weakly connected granular superconductor in response to externally applied arbitrary thermal gradient ∇T (nonlinear Seebeck effect) is considered within a model of 3D Josephson junction arrays. For ∇T>(∇T)_c, where (∇T)_c is estimated to be of the order of ≃10⁴ K/m for YBCO ceramics with an average grain size d≃10 μ m, the weak-links-dominated thermopower S is predicted to become strongly ∇T-dependent. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 650–654 (10 May 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Numerical study of multi-hole SQUIDs using Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions

The I–V characteristics and the resultant total energies have been calculated full numerically for the parallel arranged multi-hole superconducting quantum interference devices (SQUIDs) consisting of Bi₂Sr₂CaCu₂O_8+δ high-T_c superconductors intrinsic Josephson junctions (BSCCO–IJJs). It has been found that (I) the effect of charge coupling between neighboring Josephson junctions is not so important, (II) the effect of noise is not so crucial except for the case of low β_L and no external magnetic field, and (III) a reliable external magnetic field dependence is obtained when the β_L is less than about 0.5, where the β_L is a dimensionless parameter defined by L_loopI_c/Φ₀ using a loop inductance L_loop of a SQUID, a critical current I_c of a junction, and a flux quantum Φ₀. We have pointed out that (IV) the steps which differ from Shapiro steps are found when an external ac modulation current is applied to the parallel arranged multi-hole SQUIDs, and (V) the I–V characteristics of a double hole BSCCO–IJJs–SQUID trapping a flux quantum can be controlled as a function of the external magnetic field.     

Influence of transport current and thermal fluctuations on the resistive properties of HTSC+CuO composites

Measurements of the temperature dependence of the electrical resistance R(T) below the superconducting transition temperature have been performed at different values of the transport current in HTSC+CuO composites modeling a network of weak S-I-S Josephson junctions (S—superconductor, I—insulator). It has been shown experimentally that the temperature dependence R(T) at different values of the transport current is adequately described by means of the mechanism of thermally activated phase slippage developed by Ambegaokar and Halperin for tunnel structures. Within the framework of this model we have numerically calculated the temperature dependence of the critical current J _c(T) as defined by various criteria. Qualitative agreement obtains between the measured and calculated temperature dependences J _c(T). Fiz. Tverd. Tela (St. Petersburg) 41, 969–974 (June 1999)     

Temperature dependence of the critical current in YBa2Cu3O7−δ and Bi2Sr2Ca1Cu2O8 Josephson junctions

We have studied the stationary Josephson effect on YBa₂Cu₃O_7−δ (T_c=90 K) and Bi₂Sr₂Ca₁Cu₂ O₈ (T_c=80 Kand 87 Kfortwosamplesofdifferentorigin) ceramic based junctions. The temperature dependence of the critical current near T_c has been found as I_c≈(T_c-T) for the Y-Ba-Cu-O samples indicating that they should be classified as S-N-I-N-S type junctions. The I-V curves of the Bi-Sr-Ca-Cu samples show the typical behaviour of S-I-S structures. Using Ambegaokar-Baratoff's theory for Bi₂Sr₂Ca₁Cu₂O₈, the temperature dependence of the superconducting state gap Δ(T) was calculated and it was evaluated that 1.452Δ(0)/k_BT_c3.5.     

Critical current calculations for long 0-π Josephson junctions

A zigzag boundary between a $d_{x^2 - y^2}$ and an s-wave superconductor is believed to behave like a long Josephson junction with alternating sections of 0 and π symmetry. We calculate the field-dependent critical current of such a junction, using a simple model. The calculation involves discretizing the partial differential equation for the phase difference across a long 0-π junction. In this form, the equations describe a hybrid ladder of inductively coupled small 0 and π resistively and capacitively shunted Josephson junctions (RCSJ's). The calculated critical critical current density J_c(H_a) is maximum at non-zero applied magnetic field H_a, and depends strongly on the ratio of Josephson penetration depth λ_J to facet length L_f. If λ_J/L_f ≫1 and the number of facets is large, there is a broad range of H_a where J_c(H_a) is less than 2% of the maximum critical current density of a long 0 junction. All of these features are in qualitative agreement with recent experiments. In the limit λ_J/L_f →∞, our model reduces to a previously-obtained analytical superposition result for J_c(H_a). In the same limit, we also obtain an analytical expression for the effective field-dependent quality factor Q_J(H_a), finding that . We suggest that measuring the field-dependence of Q_J(H_a) would provide further evidence that this RCSJ model applies to a long 0-π junction between a d-wave and an s-wave superconductor.     

Electron transport in hybrid superconductor heterostructures with manganite interlayers

Hybrid herostructures comprising an YBa₂Cu₃O _x (YBCO) high-temperature superconductor (HTS) layer and Nb/Au low-temperature superconductor (LTS) bilayer (with critical HTS and LTS temperatures T _c and T′_c, respectively), separated by a thin (d _M = 5–20 nm) interlayer of LaMnO₃, La_0.7Ca_0.3MnO₃, or La_0.7Sr_0.3MnO₃ manganite have been studied. The electric resistance and magnetic properties of individual (evaporated directly onto the substrate) manganite films and related hybrid herostructures have been measured. Based on quasi-classical equations, analytical expressions for the conductivity of herostructures at T ≤ T′_c are obtained in the case of a low-transparency superconductor/manganite interface. It is established that the conductivity of heterostructures is determined by the proximity effect (related to the penetration of a condensate wavefunction from the Nb/Au bilayer to manganite) and depends strongly on interface transparency. At low temperatures (T ≪ T _c′), the conductivity peaks are found at voltages determined by the exchange field of the manganite interlayer. At T _c′ < T < T _c, conductivity features at nearly zero bias voltages are observed, which are related to the superconductivity of the YBCO electrode.     

Josephson current in superconductor/ferromagnet/superconductor junctions

By using the Bogoliubov–de Gennes equation and the Nambu spinor Greens function approach, we have theoretically studied the dc Josephson current and the coupling phase state of superconductor/ferromagnet/superconductor (SC/FM/SC) junctions, where the FM is of weak ferromagnetism. From the behavior of the temperature-dependent dc Josephson current (I_c), we confirm that such SC/FM/SC junction may change from 0-phase to π-phase state with increasing the temperature (T), for particular parameters of the thickness and the strength of ferromagnetism of the FM interlayer. We attribute such changement to an extra phase difference between the two SCs. The results are qualitatively consistent with an experiment [Phys. Rev. Lett. 86 (2001) 2427], which shows a sharp cusp structure on the I_c−T curves of Nb/Cu_0.48Ni_0.52/Nb junction for specific thickness of the Cu_0.48Ni_0.52, indicating the junction changes from 0-phase state at high temperatures to π-phase state at low temperatures.     

Critical currents in polycrystalline thin films of high-T c superconductors

Summary It is shown that the behaviour of the temperature dependence of the critical current in polycrystalline thin films of high-T _c superconductors depends crucially on the assumption made concerning the nature of the intergranular material. The usual assumption of a superconductor-insulator-superconductor (=SIS) ?sandwich? between each grain leads to a crossover fromI _c∼(1−T/T _c) toI _c∼(1−T/T _c)^3/2, for temperatures nearT _c (whereI _c is the critical current,T the absolute temperature, andT _c the superconducting transition temperature). Instead, for a superconductor-normal metal-superconductor (=SNS) sandwich the dependenceI _c∼(1−T/T _c)² is found for all temperatures. Consideration is given to the effect of self-magnetic field on the analysis. The comparison between expressions for continuous and granular systems is extended. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

A comparison of barrier type tunnel junction and point contact tunnel junction formed on the same highT c material

By making a combination of both point contact and barrier type tunnel junctions on a single sample of the highT _c superconductor BSCCO (2212) single crystal, we have shown that as the tunneling tip is slowly retracted from the surface a point contact junction gradually evolves from a N-S short to a high resistance tunnel junction. The scaled dynamic conductance (dI/dV) of this point contact tunnel junction becomes almost identical to that of a conventional barrier type tunnel junction and both show a linear dI/dV —V curve. The observation implies that at high resistance a point contact junction behaves in the same way as a barrier type tunnel junction. We suggested that the almost linear tunneling conductance obtained in both the cases most likely arises due to an intrinsic characteristic of the surface of the crystal comprising of a mosaic of superconducting regions of the order of a few nanometers. We also conclude that the barrierless (N-S) point contact obtained by piercing the surface oxide layer of the crystal shows Andreev reflection which we suggest as the origin of the zero bias anomaly often observed in point contact junctions.