Ferromagnet–superconductor hybrids

The new class of phenomena described in this review is based on the interaction between spatially separated, but closely located ferromagnets and superconductors, the so-called ferromagnet–superconductor hybrids (FSH). Typical FSH are: coupled uniform and textured ferromagnetic and superconducting films, magnetic dots over a superconducting film, magnetic nanowires in a superconducting matrix, etc. The interaction is provided by the magnetic field generated by magnetic textures and supercurrents. The magnetic flux from magnetic structures or topological defects can pin vortices or create them, changing the transport properties and transition temperature of the superconductor. On the other hand, the magnetic field from supercurrents (vortices) strongly interacts with the magnetic subsystem, leading to formation of coupled magnetic–superconducting topological defects.

The proximity of ferromagnetic layer dramatically changes the properties of the superconducting film. The exchange field in ferromagnets not only suppresses the Cooper-pair wavefunction, but also leads to its oscillations, which in turn leads to oscillations of observable values: the transition temperature and Josephson current. In particular, in the ground state of the Josephson junction the relative phase of two superconductors separated by a layer of ferromagnetic metal is equal to?π?instead of the usual zero (the so-called π-junction). Such a junction carries a spontaneous supercurrent and possesses other unusual properties. Theory predicts that rotation of magnetization transforms s-pairing into p-pairing. The latter is not suppressed by the exchange field and serves as a carrier of long-range interaction between superconductors.     

高温超导体中约瑟夫森涡旋流阻的振荡效应

通过数值计算耦合sine-Gordon方程组研究高温超导体中约瑟夫森涡旋的运动,得到约瑟夫森涡旋电压和流阻随平面磁场和驱动电流的变化规律.固定驱动电流,约瑟夫森涡旋电压和流阻随着磁场的增大出现周期性的振荡行为,振荡周期与每层约瑟夫森结中进入一个磁通量子相对应.分析和阐明了产生这种周期性振荡的原因. 关键词： 约瑟夫森涡旋 涡旋格子 高温超导     

Anomalous Josephson vortex solutions in Josephson junctions with multiple tunneling channels

We construct a theory for Josephson junction with multiple tunneling channels. We focus on two situations, i.e., a heterotic junction composed of two-gap-superconductor, insulator, and one-gap-superconductor, and a grain-boundary junction formed by two identical multi-gap superconductors. Then, we show that the magnetic field distribution of the Josephson vortex for ±s-wave superconductivity is much more enlarged than that for s-wave without sign change between the order parameters. We display such anomalous vortices and suggest how to evaluate the enlargement.     

Tunable supercurrent in superconductor/normal metal/superconductor Josephson junctions

When two superconductors are connected by a weak link a supercurrent flows determined by the difference in the macroscopic quantum phases of the superconductors. Originally, this phenomenon was discovered by Josephson for the case of a weak link formed by a thin tunnel barrier. The supercurrent I is related to the phase difference ϕ through the Josephson current–phase relation, I = I_csin ϕ, with I_c, the critical current, depending on the properties of the weak link. A similar relation holds for weak links consisting of a normal metal, a semiconductor or a constriction . In all cases, the phase differenceϕ =  0 when no supercurrent flows through the junction, and ϕ increases monotonically with increasing supercurrent until the critical current is reached. Using nanolithography techniques we have succeeded in making and studying a Josephson junction with a normal metal weak link, in which we have direct access to the microscopic current-carrying states inside the link. We find that the fundamental Josephson relation can be changed fromI = I_csin ϕ toI = I_csin(ϕ + π), i.e. to a π -junction, by suitably controlling the energy distribution of the current-carrying states in the normal metal. This fundamental change in the way these Josephson junctions behave has potential implications for their use in superconducting electronics as well as (quantum) logic circuits based on superconductors.     

Microwave absorption in high-Tc superconductors studied by the EPR method

Dependences of the microwave absorption on temperature, magnetic field and microwave power obtained for the high-T _c superconductors are presented. Shape of the magnetically modulated microwave absorption, low-field phase diagram and overheating of the Josephson junction system induced by microwave irradiation are discussed. The model of the Josephson junction system interacting with microwaves has been used to explain the behavior of the high-T _c superconductors in low magnetic field.     

Application of nano-scale Josephson junction as phase sensitive detector for analysis of vortex states in mesoscopic superconductors

We study phase shifts in a Josephson junction induced by vortices in superconducting mesoscopic electrodes. The position of the vortices are controlled by suitable geometry of a nano-scale Nb–Pt_1−xNi_x–Nb junction of the overlap type made by Focused Ion Beam (FIB) sculpturing. The vortex is kept outside the junction, parallel to the junction plane. From the measured Fraunhofer characteristics the entrance and exit of vortices are detected. By changing the bias current through the junction at constant magnetic field the vortices can be manipulated and the system can be switched between two consecutive vortex states which are characterized by different critical currents of the junction. A mesoscopic superconductor thus acts as a non-volatile memory cell in which the junction is used both for reading and writing information (vortex). Furthermore, we observe that the critical current density of Nb–Pt_1−xNi_x–Nb junctions decreases non-monotonously with increasing Ni concentration. It exhibits a minimum at ∼40 at.% Ni, which is an indication of switching into the π state.     

Generation of electromagnetic radiation in the motion of vortices in magnetically coupled superconducting films

We examine theoretically the generation of electromagnetic radiation in the relative motion of vortex lattices in magnetically coupled films in the dc transformer geometry. We establish the conditions under which the force of mutual pinning of the vortex lattices varies according to a harmonic law as a function of the relative displacement of the vortices in the films within a given range of magnetic field inductions. In this case the equation describing the viscous flow of vortex lattices in magnetically coupled films is the same as the equation of the resistively shunted Josephson junction model. We show that magnetically coupled superconductors exhibit the properties of a Josephson element without any restrictions on the geometrical size of such a system imposed by the coherence length ξ. The frequency f of the electromagnetic radiation generated by the relative motion of vortex lattices in magnetically coupled superconductors depends on the spatial period of the vortex lattices and the velocity of relative vortex motion, which means that the frequency of the radiation can be tuned by applying a magnetic field or a current. Zh. éksp. Teor. Fiz. 113, 1319–1338 (April 1998)     

Terahertz electromagnetic wave emission by using intrinsic Josephson junctions of high-Tc superconductors

High-Tc cuprate superconductors like Bi₂Sr₂CaCu₂O_8+y (Bi-2212) show very large anisotropy in the electrical conduction. Inside the CuO₂ plan the conduction looks like that in good metals, while the block layers located between CuO₂ planes behave like insulating barriers. Thus, neighboring CuO₂ layers are linked by the Josephson coupling in superconducting states, and the Bi-2212 single crystal can be regarded as a natural serial array of Josephson junctions along the c-axis. It has been found out that in such a system a unique excitation mode called the collective Josephson plasma exists. The mode collectively oscillates along the c-axis, while it propagates along any direction ranged from the ab-plane to the c-axis. If the mode can be coherently excited, the system should be very useful as a device generating strong electromagnetic wave emission. In this paper we review a theoretical framework describing the Josephson plasma modes. The Josephson vortex penetrates into the sample under the magnetic field parallel to the CuO₂ plane and it moves along the ab-plane under an external current parallel to the c-axis. In the vortex flow state, the vortex speed can reach and exceed the propagating velocities of the Josephson plasma modes due to very weak dissipation. Then, the vortices strongly couple with the plasma modes and change their flowing lattice configurations into patterns dependent on the interacting plasma mode profiles. Among many expected flow patterns, we pay attention to a special state resonating with a plasma mode in-phase along the c-axis because all junctions synchronize in such a state. Large-scale numerical simulations by Machida et al. confirmed that the special state characterized by the rectangular lattice stably appears in a wide range of I–V characteristics. In this paper, we report their recent simulation results.     

无序二维约瑟夫森结阵列中磁场引起的涡旋玻璃态相变

采用电阻阻错结的无序二维约瑟夫森结阵列模型,数值研究超导薄膜中垂直磁场引起的涡旋运动.通过分析磁场激发产生的涡旋度Ne及低频电压噪声S₀的变化特性,得到如下结论：在无序超导体中固定温度不变,随着磁场的减弱涡旋液态经过准有序的布拉格相,涡旋玻璃相重新进入到低磁场下的钉扎稀磁液相. 由于在涡旋玻璃相中,电流驱动下的噪声值表现出一个峰,表明系统处于无序与有序相互竞争的亚稳态,并且临界电流应有峰值效应. 计算得到噪声值的变化与Okuma等得到的无序超导Mo_xSi_1-x膜实验现象一致,并能解释磁场降低引起的重新进入钉扎的稀磁液相行为. 关键词： 约瑟夫森结阵列 磁通玻璃 重新进入 峰值效应     

Chemomagnetism,magnetoconcentration effect,and “fishtail” anomaly in chemically induced granular superconductors

Within a 2D model of Josephson junction arrays (created by a 2D network of twin boundary dislocations with strain fields acting as an insulating barrier between hole-rich domains in underdoped crystals), a few novel effects expected to occur in intrinsically granular material are predicted, including (i) Josephson chemomagnetism (chemically induced magnetic moment in zero applied magnetic field) and its influence on a low-field magnetization (chemically induced paramagnetic Meissner effect) and (ii) the magnetoconcentration effect (creation of oxygen vacancies in applied magnetic field) and its influence on a high-field magnetization (the chemically induced analogue of the “fishtail” anomaly). The conditions under which these effects can be experimentally measured in nonstoichiometric high-T_c superconductors are discussed.     

Topological objects in two-gap superconductor

We discuss the non-Abelian topological objects, in particular the non-Abrikosov vortex and the magnetic knot made of the twisted non-Abrikosov vortex, in two-gap superconductor. We show that there are two types of non-Abrikosov vortex in Ginzburg-Landau theory of two-gap superconductor, the D-type which has no concentration of the condensate at the core and the N-type which has a non-trivial profile of the condensate at the core, under a wide class of realistic interaction potential. We prove that these non-Abrikosov vortices can have either integral or fractional magnetic flux, depending on the interaction potential. We show that they are described by the non-Abelian topology π₂(S ²) and π₁(S ¹), in addition to the well-known Abelian topology π₁(S ¹). Furthermore, we discuss the possibility to construct a stable magnetic knot in two-gap superconductor by twisting the non-Abrikosov vortex and connecting two periodic ends together, whose knot topology π₃(S ²) is described by the Chern-Simon index of the electromagnetic potential. We argue that similar topological objects may exist in multi-gap or multi-layer superconductors and multi-component Bose-Einstein condensates and superfluids, and discuss how these topological objects can be constructed in MgB₂, Sr₂RuO₄, ³He, and liquid metallic hydrogen.     

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.     

Pinning of planar vortices and magnetic field penetration in a three-dimensional Josephson medium

The behavior of planar (laminar) vortices in a three-dimensional, ordered Josephson medium as a function of the parameter I, which is proportional to the critical junction current and the cell size, is investigated with allowance for pinning due to the cellular structure of the medium. The minimum possible distances between two isolated vortices are calculated. A system of vortices formed in a sample in a monotonically increasing external magnetic field is analyzed. The minimum distance from the outermost vortex to the nearest neighbor is proportional to I ^−1.1. For I⩽1.3 each vortex contains a single flux quantum Φ₀, and the distance between them does not decrease in closer proximity to the boundary but remains approximately constant, implying that the magnetic field does not depend on the coordinate in the region penetrated by vortices. These facts contradict the generally accepted Bean model. The sample magnetization curve has a form typical of type II superconductors. Allowance for pinning raises the critical field H _c and induces a sudden jump in the curve at H=H _c. Zh. Tekh. Fiz. 67, 38–46 (September 1997)     

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.     

Effect of vortex pinning by point defects on the lower critical field in layered superconductors

The lower critical field H _c1 in layered superconductors is calculated under the assumption that vortex pinning by point defects is strong in these materials. We consider the case of a purely electromagnetic coupling of vortex pancakes and the case of both the electromagnetic and Josephson couplings of the pancakes in a vortex line. In the latter case, singularities in the temperature dependence of H _c1 are predicted at certain characteristic temperatures.     

Induced motion of a fast Josephson vortex

A relation is established between the transport current flowing through the entire S ₁ IS ₂ WS ₃ layered structure and the velocity of a fast vortex. The fast vortex exists when the Swihart velocity in the waveguide is significantly higher than that in the Josephson junction. It is demonstrated that the main contribution to the Lorentz force that induces the vortex motion is due to the current flowing through the waveguide and skin layers of the adjacent superconductors.

     

Polarization effects induced by a magnetic field in intrinsically granular superconductors

Based on the previously suggested model of nanoscale dislocation-induced Josephson junctions and their arrays, we study the magnetic-field-induced electric polarization effects in intrinsically granular superconductors. In addition to the new phenomenon of chemomagnetoelectricity, the model also predicts a few other interesting effects, including charge analogs of Meissner paramagnetism (at low fields) and a “fishtail” anomaly (at high fields). The conditions under which these effects can be experimentally measured in nonstoichiometric high-T_c superconductors are discussed.     

Effect of Cherenkov dissipation on vortex velocity in a waveguide-coupled Josephson junction

A motion of slow and fast vortices in a waveguide-coupled Josephson junction induced by a transport current flowing through the entire structure is studied; the coupling is not assumed to be weak. For a fast vortex, conditions are established under which current oscillations due to energy dissipation via Cherenkov radiation of Swihart waves become comparable to the current compensating for ohmic losses in the Josephson junction, waveguide, and adjacent superconductors. For a slow vortex, it is proved that intermediate and strong couplings of the Josephson junction to the waveguide shift current oscillations to the velocity range below the Swihart velocity of the Josephson junction.     

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.     

Numerical research on RF induced zero-crossing steps of stacked Josephson junction in flux-flow state

RF responses of intrinsic Josephson junction stacks in the flux-flow state have been studied to explore vortex motion. We have reported various RF induced effects on flux-flow of Bi₂Sr₂CaCu₂O_8+y intrinsic Josephson junctions. In a pinning free state, a remarkable zero-crossing step appears at a certain voltage on I–V curve, which is closed to the voltage V = NΦ₀f, where N is the number of junction, Φ₀ is the flux quantum, f is the RF frequency, respectively. It is shown that vortex motion phase-locked to external microwaves play an important role in the responses. In this report, we have carried out numerical simulation by using the coupled sine-Gordon equations in order to compare with the experimental results. The numerical simulations reveal that the alternating magnetic field of microwaves drives vortices into the stack and generates the zero-crossing step.