Hall Tunneling of Vortices in Superclean Superconductors

We discuss the main features of Hall tunneling of pancake vortices in superclean high-T _c superconductors. The general formalism for the calculation of the lifetime of a vortex pinned in a metastable configuration is described. The results are applied to the problem of quantum tunneling of a pancake vortex from a columnar defect in the limit of a small driving current.     

Vortices with Fractional Flux Quanta in Multi-Band Superconductors

In superconductors with three or more components, time-reversal symmetry may be broken when the inter-component couplings are repulsive, leading to a superconducting state with twofold degeneracy. When prepared carefully, there is a stable domain wall on a constriction which connects two bulks in states with opposite chiralities. Applying external magnetic field, vortices in different components dissociate with each other, resulting in a ribbon shape distribution of magnetic field at the domain wall.     

Vortices in Hubbard Superconductors: A Bogoliubov-de Gennes Approach

Based on the Bogoliubov-de Gennes formalism, we study vortices with quantum magnetic fluxes in two-dimensional supercells, when an external magnetic field (B) is applied to s-, d-, and anisotropic s-wave superconductors. This study is carried out by using a generalized Hubbard model including negative U and V, as well as a nearest-neighbor correlated hopping interaction (Δt). The self-consistent calculation of the superconducting gap (Δ) shows the formation of vortices in real space, whose structure depends on the electron-electron interaction. Furthermore, the supercell averaged Δ as a function of B reveals qualitatively different behaviors for the three analyzed pairing interactions. Finally, the results suggest that the d-wave superconducting states have larger second critical magnetic fields than those corresponding to isotropic and anisotropic s-wave ones.     

Dynamical Phase Diagram of Driven Vortices in High-T c Superconductors

Large-scale simulations on the current-driven three-dimensional frustrated anisotropic XY model with resistively-shunted junction dynamics have been performed to study the dynamical phase diagram in high-T _c superconductors. With the decrease of the current, a moving smectic is found between a moving Bragg glass and a moving liquid at high temperatures. The first-order phase transition between the moving Bragg glass and the moving smectic is clarified. At low temperatures, the moving Bragg glass can crossover to the (creeping) Bragg glass directly. Interestingly, at very high currents, the moving Bragg glass is replaced by a highly disordered phase due to the activation of vortices and anti-vortices.     

Quantized Vortices and Diamagnetic Precursor to the Meissner State in High-T c Superconductors

We report the magnetic imaging for underdoped and optimally-dopedLa_2–x Sr _x CuO₄ (LSCO) thin films on single substrates and nearly optimallydoped YBa₂Cu₃O_7–x (YBCO) thin films on tricrystal substrates in the temperature range both below and above T _c using scanning SQUID microscopy. Below T _c, clear integer- and half-integer quantized vortices were observable. Above T _c, however, the inhomogeneous diamagnetic domains appeared. The local diamagnetic domains that led to the Meissner state were found in the broad temperature range for underdoped samples and in the narrow limited temperature range for optimally-doped samples. The results provide evidence that local diamagnetic domains are closely related to the pseudogap state. The continuous connection of the domain state above T _c with the state of a half-integer vortex at the tricritical point in the YBCO film below T _c also indicates that the diamagnetic domains are also closely related to the occurrence of d_x ^{2-y 2}-wave superconductivity.     

Lorentz Microscopy Observation of Unconventional Behaviors of Vortices in High-T c Superconductors

Vortices in high-T _c superconductors have been predicted to behave in unconventional manners that reflect the layered structure of the materials. Our newly developed 1-MV field-emission electron microscope has opened the way to enable individual vortices to be observed inside high-T _c superconducting thin films. This makes it possible to investigate the inner structures of vortices, such as those trapped along tilted columnar defects and those of chain vortices that are formed when a magnetic field is obliquely applied with respect to the normal of the layer plane of the materials.     

Spontaneous Generation of Single Vortices and Anti-Vortices in Superconductors with Restricted Geometries

We study the nucleation of vortices in a thin (thickness ≪ penetration depth) mesoscopic superconducting disc in an applied magnetic field perpendicular to the disc (i.e., parallel to the axis of the disc). We write down an expression for the free energy of the system with an arbitrary number of vortices and anti-vortices at finite (non-zero) temperatures. For a given applied field, we minimize the free energy to find the optimal position of the vortices and anti-vortices (the configuration which minimizes the energy). We show that, whereas at zero temperature anti-vortices do not nucleate, anti-vortices do penetrate the disc at finite temperatures. We also calculate the magnetization of the disc as a function of the applied field and hence determine the different configurations possible in which a fixed number of fluxoids can penetrate the disc.     

Josephson Vortices in Weakly-Coupled Superconductors as Topological Solitons of the Sine-Gordon Equations for Phase Differences

No Heading We present a mathematically rigorous solution of the problem of magnetic properties of weakly-coupled superconducting multilayers with an arbitrary number N 2 of superconducting layers in external parallel magnetic fields H > 0. By minimizing a relevant Gibbs free-energy functional, we show that the equilibrium vortex structure is given by a new class of soliton solutions: namely, topological solitons of a system of N – 1 coupled static sine-Gordon equations for the phase differences in a finite spatial interval I = [–L,L]. A complete classification of the new soliton solutions is presented. For N = 2, 3, and N = , exact, closed-form analytical expressions are derived. The special case L = , H = 0 is considered separately. Non-soliton solutions are also analyzed: they are shown to be saddle points of the Gibbs free-energy functional. A comparison with the experiment is drawn.PACS numbers: 03.75.Lm, 05.45.Yv     

Noise-Assisted Microwave Up-conversion by Vortices in Thin-Film Superconductors with a dc-Biased Washboard Pinning Potential

So far the main theoretical basis for understanding and optimization of the microwave properties of vortices in type II superconductors has been relying upon the Coffey–Clem (CC) approach for the linear impedance at nonzero temperature. However, the CC model does not account for the non-linear response and the possibility to control it by changing the value of the dc transport current in a superconducting sample. For this reason, we have exactly solved the Langevin equation for the two-dimensional non-linear vortex dynamics in a dc bias-tilted cosine pinning potential in the presence of an ac current of arbitrary amplitude and frequency ω and have, thereby, substantially generalized the CC results. In this work we analyze the behavior of the non-linear response on kω-frequency in a wide range of dc and ac current densities, ω, and temperature. The kω-response is found to depend strongly on all these parameters, as exemplified for the third-harmonic (k=3) transformation coefficient Z ₃. The parametric window for the most enhanced up-conversion is presented. The predicted effects can be experimentally verified in thin-film superconductors with some pinning potential of the washboard type.     

Lateral Force and Lateral Connection Stiffness of Flux Pinned Docking Interface

Another novel flux pinned docking interface consisting of an YBCO high temperature superconductor bulk and two electromagnets is designed in order to improve the connection stiffness of this docking interface and the detailed control strategy of the docking process is introduced. Using this novel docking interface, two spacecraft modules appear with a noncontacting connection status through intervehicle interaction, but with the characteristics of passive stability. The identical current loop model is proposed based on the Ampere current loop hypothesis to treat the magnetic field of the cylindrical permanent magnet that may be installed in the flux pinned docking interface, and the improved image dipole model is adopted with the intention of analyzing the flux pinned lateral force of the novel docking interface theoretically. Additionally, the experiment data of the flux pinned lateral force between a YBCO high temperature superconductor bulk and a cylindrical NdFeB permanent magnet is collected. The theoretical calculation and experimental data both show an initial decrease then increase with the increase of lateral displacement. Moreover, the theoretical analysis compared to the corresponding experimental data indicates that the improved image dipole model is an effective approach. Furthermore, the flux pinned lateral connection stiffness is obtained based on Hooke’s law, showing that this stiffness initially decreases then increases as the lateral displacement that is larger than zero increases.     

Axial Force and Passive Stability of a Flux Pinned Space System

A novel mechanism of space system based on flux pinning is utilized potentially because flux pinning takes a number of advantages, such as no-mechanical connection and the characteristics of passive stability. In this novel structure, a flux pinned interface is generally composed of a high temperature superconductor and a permanent magnet or an electromagnet mounted on a respective module. In addition, a feasible type of flux pinned docking interface is designed with detailed control strategy. The improved image-dipole model is proposed with intention to calculate the flux pinned axial force between two flux pinned modules, so the axial force can be calculated analytically. In case of zero filed-cooling experiment and field-cooling experiment, the improved version of model is in good agreement with the experimental data measured in our simple experimental device. Furthermore, the potential force and damper model for a flux pinned space system is proposed, so the passive stability of the flux pinned space system is validated in sense of Lyapunov stability.     

The Maximum Levitation Force of High-T c Superconductors

In this paper we present the dependence of the maximum levitation force (F _z ^max) of a high-T _c superconductor (HTS) on the structural factors of high-T _c superconducting systems based on the Bean critical state model and Ampère’s law. A transition point of the surface magnetic field (B _s ) of a permanent magnet (PM) is found at which the relation between F _z ^max and B _s changes: while the surface magnetic field is less than the transition value the dependence is subject to a nonlinear function, otherwise it is a linear one. The two different relations are estimated to correspond to partial penetration of the shielding currents inside the superconductor below the transition point and complete penetration above it respectively. The influence of geometric properties of superconductors on the dependence is also investigated. In addition, the relation between F _z ^max and the critical current density (J _c ) of the HTS is discussed. The maximum levitation force saturates at high J _c . An optimum function of the J _c and the B _s is presented in order to achieve large F _z ^max.      

An Inverse Problem for the ac Magnetic Force Microscopy of Superconductors

A basic inversion problem for the magnetic force microscopy (MFM) of a semiinfinite superconductor in the Meissner state is formulated, ac Detection is assumed, with the MFM tip oscillating at angular frequency Ω. The coupling of all electrodynamic fields is treated, including a normal-current density in the superconductor. Under certain assumptions on the tip and superconductor geometry, a unique penetration depth λ(z) can be recovered from onedimensional force gradient measurements. This development opens new possibilities for the nondestructive evaluation of superconducting crystals and films.     

Influences of Permanent Magnets Temperature Characteristic on the Levitation Force of YBaCuO Bulk Superconductors

Influences of the temperature characteristic of sintered SmCo and NdFeB permanent magnets (PM) on the levitation force of YBaCuO bulk superconductor have been investigated in this paper. It is found that for a NbFeB PM and a SmCo PM which have the same geometric parameters, a larger influence on the levitation force of a temperature decrease of the NdFeB PM has been found. The maximum change of levitation force is as high as 47.6% at a gap of 2?mm between the bottom surface of NdFeB PM and the top surface of YBaCuO bulk when the temperature of the NdFeB PM decreases from room temperature to 77?K. This work provides basic data for high temperature superconducting levitation system measurements.     

Effect of Dissipation on Quantum Tunneling of Vortices in Tl2Ba2Ca2Cu3O10+δSuperconductors

The temperature and magnetic field dependence of the magnetic relaxation rate has been investigated at low temperatures (1.8 < T < 10 K) on two Tl₂Ba₂Ca₂Cu₃O_10+δ samples (epitaxial thin film and sintered pellet). The temperature dependence gives evidence of a crossover in the mechanism of vortex motion, from classical thermal activation to quantum tunneling as temperature decreases. The field dependence of the relaxation rate indicates a crossover in the dimensionality of vortices, from three-dimensional flux lines to two-dimensional pancake vortices as field increases. For the thin film, the temperature dependence of the rate has been fitted to the theoretically predicted expressions for finite-temperature enhancement of the quantum rate in different regimes of dissipation. In spite of the similarity of the fits, the estimate of the ratio of Hall to viscous drag terms in the equation of motion indicates that quantum tunneling in this system occurs in an intermediate dissipative regime, where both terms contribute to the motion of vortices.     

Effect of Na-dopant on the Levitation Force of Single Domain YBCO Bulk Superconductors Fabricated by TSMTG Process

Na-doped single domain YBa_2−x Na _x Cu₃O_7−δ (YBCO, x=0.05, 0.1, 0.15, 0.2, 0.25, 0.3) bulk superconductors were prepared by a modified melt textured process and the effect of Na substitution on the levitation force of YBCO bulks have been investigated. The maximum levitation forces (MLF) are much different for samples with a different Na element content. It is found that the optimum Na element content in YBCO for the strong MLF is around x=0.2. It is also found that the addition of Na could reduce and increase the ATH of the YBCO platelet while x less than 0.1 and larger than 0.1, some of adjacent platelet grains are well intergrown each other in the sample with x=0.2 comparing to the other samples and the influence of the Na addition on the Y211 particle size is not obvious.     

Vortices in superconductors

In type II superconductors where the London penetration depthλ is larger than the coherence lengthξ, there is a possibility of flux penetration inside the sample for magnetic field greater than \(H_{0_1 } \left( { = \frac{{\phi _0 }}{{4\pi \lambda ^2 }}ln \lambda /\xi , \phi _0 = \frac{{hc}}{{2e}}} \right).\) The flux penetrates in the form of vortices with core of sizeξ. However these vortices differ from those in superfluid He⁴ in variation of currentj(r) circulating around them. For superconductorsj(r) ～ 1/r only up to a distanceλ and then it falls exponentially whilev(r) ～ 1/r for all distances in superfluids. The reason is that in superconductors vortex carries a magnetic flux which is screened by conduction electrons. This coupling of order parameter field (the pairing wavefunction) with the gauge field has many interesting implications for superconductors and for non-Abelian gauge theories. Some examples are as follows:

1. The energy of the vortices is reduced. The energy of vortex of lengthL (ind = 3 sample) is of orderL lnL for a superfluid, is of orderL in a superconductor, and (in ad = 2 sample) the energy of a vortex point which diverges like lnR (whereR is the size of the sample) in a superfluid becomes finite in a superconductor.
2. The superconducting-normal transition in three dimension is very weak first order, because the fluctuations of the gauge field, when summed over, add to Ginzburg Landau free energy a term proportional to |ψ|³, whereψ is the order parameter.
3. Because of the lnr behaviour of interaction energy of vortices, a two-dimensional superfluid sample can exhibit a Kosterlitz-Thouless type transition whereas a strictlyd = 2 superconductors should not have any. However for dirty superconducting films whereλ is large vortex binding-unbinding transition can be observed with quite a rich phase diagram.

The paper presented at the discussion meeting discusses the above in detail. Here we give only a brief summary of results and some relevant references.     

Effect of Magnetic Flux Distribution and Magnetic Powder Addition on the Magnetic Levitation Force of Sm123 Superconductors

Sm123 and Sm211 were prepared by melt-powder-melt-growth and solid-state-reaction techniques, respectively, to have the nominal composition of (Sm123)_0.75(Sm211)_0.25. After the preparation of this composition, the Fe-B magnetic powder (MP) was added to the composition for 0.000, 0.010, 0.015, 0.025, 0.050 wt.% to investigate the effect of MP addition on the levitation force density (LFD). Additionally, different permanent magnets (PM) were used as magnetic-field source to investigate the effect of magnetic-field gradient on the LFD of MP added superconductors. Our findings indicate that the MP addition acts as a flux pinning centre in the sample and enhances the LFD up to 0.025 wt.% adding amount, and the optimum flux gradient which produces a screening current in the sample occurs when the B/d (magnetic-field intensity/ diameter of PM) ratio is equal to 0.060. These results imply that the experimental data can be useful for fabricating process of superconducting samples with larger MLF values, and designing of superconducting magnets, flywheel energy storage and maglev systems.     

Effect of Pre-magnetization on Quasi-static Force Characteristics in a Space Superconducting Interface Structure Adopting High T c Superconductors

Flux-pinned interaction between high T _c superconductors (HTSs) and an applied magnetic field provides a new, no-contact interface approach that can be used in docking and assembling process of space module systems. Unlike operations on the Earth, the magnetization of the HTS happens in orbit which differs from the traditional field cooling (FC) magnetization, and the additional field has to be used to magnetize the HTS in advance and make it produce a self-stable force in the interacting process with the interfacing magnet. This paper presents a type of superconducting interface structure configuration consisting of bulk HTSs, actuation electromagnets and interfacing magnets, and discusses the effects of different magnetization conditions on the quasi-static force interaction between the HTS and the interfacing magnet. Primary experiments show that the HTS after pre-magnetization can show self-stable force behavior, which often happens in the traditional FC magnetization, and the self-stable force is further enhanced with the increase of the pre-magnetizing current. Multi-pulse field magnetization after the pre-magnetization is also applied to raise the trapped field strength (B _T ) of the superconductor. The results show that B _T is added with the increasing number of the pulsed field, and the corresponding self-stable force properties are also improved. Therefore, the pre-magnetization combined with the pulsed field magnetization can enhance the flux trapping in the HTS and bring more stable force for the superconducting interface structure.