Defect Pinning and Critical Current of Magnetic Vortex Cluster in Mesoscopic Type-1.5 Superconductors

Cadorim L.R., Sardella E., Domínguez D., Berger J.

Maksimova A., Moroz A., Rudnev I., Pokrovskii S., Kashurnikov V.

Abstract Current–voltage characteristics of a superconductor with tilted irradiation defects in a dc magnetic field have been calculated using the Monte Carlo method in the framework of the three-dimensional model of a layered high-temperature superconductor (HTS). The dependences of the critical current on the magnitude of the external magnetic field have been calculated from the current–voltage characteristics using the 1 μV/cm criterion. The defects were tilted both along the direction of vortex entry into the sample (the x-direction) and perpendicular to it (the y-direction). It has been shown that these dependences have weak maxima near the lower critical field for defects tilted along the x-axis. There were no such maxima for non-tilted defects. Defects tilted along the y-axis were more effective for enhancing the critical current of the HTS under study.

Maksimova A.N., Gokhfeld D.M., Moroz A.N., Kashurnikov V.A.

Vortex relaxation has been studied in a microsized HTS with various distributions of artificial pinning in the form of submicro-holes. It has been shown that, in some cases, for a superconductor with dimensions up to several micrometers, the time dependences of the trapped magnetic field do not correspond with the collective creep model. The dependences of the trapped-field relaxation rate and vortex activation energy on the magnetizing field (up to 0.5 T) and temperature (up to 50 K) have been obtained. It has been shown that the presence of submicro-holes slightly increases the relaxation rate, mainly due to the decrease in the number of random nanosized pinning centers.

Benites T.N., Presotto A., Barba-Ortega J., Sardella E., Zadorosny R.

Abstract All superconductor applications lie on carry dissipationless current; however, in the presence of external magnetic fields, including the self-field, vortices penetrate the sample, and their dissipative motion generates resistive states. Thus, once the superconducting state survives for higher magnetic fields due to the presence of vortices, those specimens cannot move to increase the material’s critical current density; thus, in this work, we studied the influence of surface defects on the vortex penetration at square mesoscopic superconducting materials using the time-dependent Guinzburg-Landau framework. The lateral size of the samples was 12 times the coherence length at zero Kelvin, with defects distributed in two opposite borders. The main result showed that the currents crowd around the surface defects are responsible for vortex penetration at 60% of critical temperature.

Ryu Y.G., Om J.H., Kim J.H., Ro G.I., Mun G.I., Hong S.

In the present work, the influences of surface defects on the motion of magnetic vortices in a mesoscopic type-II superconductor with randomly distributed pinning centers are considered using the time-dependent Ginzburg-Landau equations. Two kinds of surface defects are located in the boundary: first, the pinning centers. and second, the geometric defects simultaneously with pinning centers. In the simulation, the magnetization curves, vorticity, and the density of superconducting electrons for both different contents of pinning centers and various geometric defects are analyzed. For the pinning centers as surface defects, the maximum magnetization values as a function of the contents exponentially decrease, and the field $$H_1$$ where the first vortex penetrates and the field $$H_2$$ where the complete transition from superconducting to a normal state in the system occurs is reduced. For the geometric defects as surface defects, the density of superconducting electrons and the magnetization curves depend on both size and form of them. In addition, a threshold on the size of geometric defects in which the motion of vortices and vorticity changes is presented.

Moroz A., Rudnev I., Stepanenko A., Maksimova A., Kashurnikov V.

Current-voltage characteristics have been calculated for a high-temperature superconductor containing triangular and square periodic arrays of pinning centers with various disorder rates. Non-monotonic dependences of critical current density on the disorder rate have been obtained for the triangular lattice, showing that a perfectly ordered lattice provides smaller critical currents than that with minor distortions, especially at high magnetic fields. For the square lattice, the critical current was mostly declining, with minor peaks at small disorder rates. A thorough analysis of the vortex dynamics has been done, showing the differences in the way vortices move through the disordered lattice and how their paths affect the critical current density.

Salamone T., Hugdal H.G., Jacobsen S.H., Amundsen M.

We present a mechanism allowing for superconductivity at high magnetic fields, beyond the Pauli-Chandrasekhar-Clogston limit. We consider spin splitting induced by an in-plane external magnetic field in a superconductor with two relevant bands close to the Fermi level. The magnetic field therefore controls which bands are available for Cooper pair formation. The presence of interband superconducting pairing, i.e., Cooper pairs formed by electrons with different band indices, produces high-field reentrant superconducting domains, whose critical magnetic field violates the Pauli-Chandrasekhar-Clogston limit. We analyze how the interband superconducting domains are influenced by the band parameters, and show that, for a certain range of parameters, the system presents two separate superconducting regions, for low and high magnetic field.

Cadorim L.R., de Toledo L.V., Ortiz W.A., Berger J., Sardella E.

By using the full 3D generalized time-dependent Ginzbug-Landau equation, we study a long superconducting film of finite width and thickness under an applied transport current. We show that, for sufficiently large thickness, the vortices and the antivortices become curved before they annihilate each other. As they approach the center of the sample, their ends combine, producing a single closed vortex. We also determine the critical values of the thickness for which the closed vortex sets in for different values of the Ginzburg-Ladau parameter. Finally, we propose a model of how to detect a closed vortex experimentally.

Ryu Y.G., Mun G.I., Kwon Y.N., Kim S.H., Hong S.

• A study on motion of magnetic vortices in type-Ⅱ superconductor with randomly distributed pinning centers of normal state. • The maximum magnetization values decrease exponentially as the content ω increases. • The content of pinning centers with the largest mixed state is ω =0.2. The dynamic behaviors of the magnetic vortices in a two-dimensional square superconductor with randomly distributed pinning centers of normal state were considered using the Ginzburg-Landau (G-L) model. The pinning centers are randomly distributed as various contents in all the area of the superconductor and a distribution function p( r ) defined in a MATLAB is used to determinate the size and sites of normal state pinning centers. Using COMSOL and MATLAB, we analyzed the magnetization curves and the density of superconducting electrons as a function of the external magnetic field applied along the z-axis. Simulation results showed that the vortices configurations and magnetization depend on the content of the pinning centers and the maximum magnetization values decrease exponentially as the content increases. The content of pinning centers with the largest mixed state is determined by modeling the number of the magnetic vortices trapped in the pinning centers. This work will provide good results into understanding the dynamics of the magnetic vortices in a superconductor with randomly distributed pinning centers in view of the circumstance that they are randomly distributed in the superconductor during fabricating it.

Gokhfeld D.M., Maksimova A.N., Kashurnikov V.A., Moroz A.N.

• The flux trapped in a superconducting plate with perforations depends on the number, diameter, pinning potential of holes, and the pinning potential of defects. • It is possible to maximize the trapped flux by tuning the size and position of holes. • The maximal reachable value of the trapped flux depends only on the ratio of pinning potentials of the holes and defects. The use of artificial holes can improve the performance of high-temperature bulk superconductors. We report the results of Monte Carlo simulations of the trapped magnetic flux in superconducting samples with different configurations of perforated holes. Vortex trapping and emission at the hole boundary were modeled to account for flux pinning on the holes. It was found that the trapped flux can reach its maximum value, which does not depend on the number of holes. The dependence of the trapped flux on the diameter and number of holes is explored and described by the suggested relations that account for pinning on the holes and the effective hole area. Recommendations are provided to attain the maximum trapped flux for a fixed number or diameter of holes.

Du S., Zhong Y., Yao S., Peng L., Shi T., Sang L., Liu X., Lin J.

Two-band mesoscopic superconductors are known to exhibit specific vortex states. In this paper, finite element method (FEM) is used to numerically solve the time-dependent Ginzburg-Landau (TDGL) equation with s+d wave coupling for a 3D mesoscopic superconducting strip. We discuss the effect of external magnetic field H and applied current I on s+d wave coupling at the temperatures T s < T < T d , where T s and T d are the critical temperatures of s- and d-bands, respectively. The obtained results show that this coupling is enhanced by the applied current and reflected by the vortex dynamics in two bands. A small amount of Cooper pairs in the s-band form a series of different vortex and antivortex states. Mutual attraction of vortex and antivortex induces simultaneous motion of s- and d-vortices at applied current I . This work provides theoretical background for the design of mesoscopic superconducting devices. • Finite element method is used to numerically solve the two-band time-dependent Ginzburg-Landau equation. • The coupling between s- and d-waves is investigated in a two-band 3D superconducting strip. • The effect of applied current, external magnetic field, weak link on the s- and d-vortices interaction was studied. • Mutual attraction of vortex and antivortex induces simultaneous motion of s- and d-vortices at applied current.

Aguirre C.A., Joya M.R., Barba-Ortega J.

We solve the two-band Ginzburg-Landau equations for a superconducting mesoscopic prism for a condensate characterized by two order parameters ( ψ 1 , ψ 2 ) . We study the effect of the phase and γ ˜ differences on the vortex state, magnetization, magnetic susceptibility ( χ m ) , vortex localization, and vorticity for boths condensate. Finally, we present shown how the vortices form conglomerates in the superconductor sample states of fractional vorticity in the system for different external magnetic fields.

Yao S., Peng L., Lin J., Chen J., Cai C., Zhou Y.

Using a finite element method to numerically solve the time-dependent two-band Ginzburg–Landau model whereby setting the temperature T close to the critical temperature Tc, we studied the properties of vortex configurations of the mesoscopic two-band superconducting squares. Our analysis takes into account the relationship between the model parameters and microscopic material parameters. Especially, we analyze the effect of Fermi velocities on the vortex states in the mesoscopic two-band superconducting squares. From the simulation results, we observed four types of vortex regions in the magnetization curve for the systems, which could help to understand and detect the vortex states in mesoscopic two-band superconductors.

Oripov B., Anlage S.M.

We apply time-dependent Ginzburg Landau (TDGL) numerical simulations to study the finite frequency electrodynamics of superconductors subjected to intense rf magnetic field. Much recent TDGL work has focused on spatially uniform external magnetic field and largely ignores the Meissner state screening response of the superconductor. In this work, we solve the TGDL equations for a spatially non-uniform magnetic field created by a point magnetic dipole in the vicinity of a semi-infinite superconductor. A novel two-domain simulation is performed to accurately capture the effect of the inhomogeneous applied fields and the resulting screening currents. The creation and dynamics of vortex semiloops penetrating deep into the superconductor domain is observed and studied, and the resulting third-harmonic nonlinear response of the sample is calculated. The effect of point-like defects on vortex semi-loop behaviour is also studied. This simulation method will assist our understanding of the limits of superconducting response to intense rf magnetic fields.

Vadimov V.L., Silaev M.A.

We show that multiband superconductors with broken time-reversal symmetry can produce spontaneous currents and magnetic fields in response to the local variations of pairing constants. Considering the iron pnictide superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$ as an example we demonstrate that both the point-group symmetric $s+is$ state and the C$_4$-symmetry breaking $s+id$ states produce in general the same magnitudes of spontaneous magnetic fields. In the $s+is$ state these fields are polarized mainly in ab crystal plane, while in the $s+id$ state their ab-plane and c-axis components are of the same order. The same is true for the random magnetic fields which are produced by the order parameter fluctuations near the critical point of the time-reversal symmetry breaking phase transition. Our findings can be used as a direct test of the $s+is/s+id$ dichotomy and the additional discrete symmetry breaking phase transitions with the help of muon spin relaxation experiments.