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The discovery of nematic triplet superconductivity in doped topological insulators CuxBi2Se3 triggers interest in the identification of the d-vector of the triplet, which is related to the antinodal direction of the gap function and determines whether the superconductor is topological. We perform self-consistent analysis of the vortex state properties in a nematic spin-triplet px-wave superconductor. We first derive a Ginzburg-Landau theory to determine the shape of the vortex and vortex lattice. We find the spatial profile of the isolated vortex is elongated along the antinodal direction, and the vortex lattice is a distorted triangular lattice elongated along x, becoming square in the specific case of a small circular Fermi surface. Finally, we calculate the local density of states self-consistently for an isolated vortex and the vortex lattice using the microscopic Bogoliubov-de Gennes equation. We find that the profile of the local density of states at low in-gap energies is always elongated along the antinodal direction. Our findings are valuable for the experimental detection of the antinodal direction of the gap function in nematic triplet superconductors, and subsequently the identification of the topological character of the superconducting state as in CuxBi2Se3. [ABSTRACT FROM AUTHOR]

It is well known that the interaction between defect-induced strain field and vortex lattice (VL) gives rise to vortex pinning behaviors. Likewise, magneto-elastic (ME) interaction is caused by the difference between specific volumes of normal phase and superconducting (SC) phase. Acting as inhomogeneous strain sources, the normal-state vortex cores produce local deformation in the surrounding SC matter and thus affect VL energy. ME interaction belongs to the fundamental physics of interdependences between vortex matter and crystal lattice. The review starts with the effects of ME interaction on magnetization, vortex morphology and intervortex interaction. In Sect. 2, theoretical descriptions of ME interaction are classified in terms of different simplifications. The core ideas and outstanding results of these theories are given. It is followed by Sect. 3, where the correlation and difference between ME and pinning interaction are outlined. Although pinning differs from ME interaction in their formation mechanisms, the pinning interaction is established upon the vortex-induced strain field from Ginzburg-Landau (GL) viewpoint. Section 4 goes further with the GL treatment for solving ME and pinning problem; the general thoughts and steps can be found in this section. The last section gives some outlooks which involve pressure dependence of Tc and anisotropy. [ABSTRACT FROM AUTHOR]

The importance of type-II superconductors with strong pinning comes from their ability to carry large transport currents in the presence of a magnetic field. We report on the results of the bulk magnetization measurements in the superconducting state in clean single crystals of NdFeAsO 0.9 F 0.1 at various temperatures. The zero-temperature superconducting critical current density, J c , where the superconducting transition temperature T c reaches a maximum of 45(1) kelvin, displays a remarkable high value. The field dependence of the critical current density was analyzed within the collective pinning model. A remarkably good agreement between the experimental results and theoretical δ1 pinning curve is obtained. This indicates that pinning in NdFeAsO 0.9 F 0.1 crystal originates from spatial variation of the mean free path. Additionally, the normalized pinning force density, F p , curves verses H/H irr (H irr is the irreversibility field) were scaled using the Dew-Hughes model. Our analysis suggests that point pinning alone cannot explain the observed field variation of F p . [ABSTRACT FROM AUTHOR]

We studied the force and potential for the vortex around moat corner as an example of the concave edge of the superconducting film by the numerical calculation method. Vortex behavior is one of the significant factors that determine the characteristics of superconducting devices. In some simple cases, such as a straight line with a constant width, the potential for the vortex can be calculated analytically using the method of images. On the other hand, it is difficult to apply such method to arbitrary-shaped films, for example, constricted nanobridges, and moats in single-flux-quantum circuits. Control of the vortex motion is very important for such devices. We have been studying the vortex behavior by numerical calculation using the time-dependent Ginzburg–Landau equation. Vortex around the straight edge moved to the moat and accelerated with a trajectory vertical to the edge. On the other hand, vortex around the corner (concave edge) moved to the moat avoiding the corner. We calculated the force and potential distribution for the vortex inside the superconducting film. The force acting to the vortex was found to be smaller around the corner compared with that around the moat side. Such behavior was understood by the difference of the vortex distortion. [ABSTRACT FROM PUBLISHER]

We studied the strong-coupling effect upon an isolated vortex in a two-dimensional chiral p-wave superconductor. We solved the Eilenberger equation for the quasiclassical Green's functions and the Éliashberg equation with single-mode Einstein boson self-consistently. We calculated the free energy of each obtained vortex and found that a non-axisymmetric vortex metastably exists in some situation. [ABSTRACT FROM AUTHOR]

It has been theoretically proposed that the enhancement of the critical current density ( J c ) through dispersing the angle of columnar defects should be greater than that of parallel columnar defects. Yet, the complication caused by decrease in pinning owing to vortex-field misalignment upon tilting of columnar defect makes it a crucial task to determine the optimal splay angle in order to fully take advantage of enhanced pinning among splayed systems. Using Ba 0.6 K 0.4 Fe 2 As 2  as a target material, we probe the effects of various splay angles on J c and determine that the ‘optimal-angle’ lies within the small angle range ( 0 -- 10 ∘ ). [ABSTRACT FROM AUTHOR]

We investigated the dissipative regime of the Bi 2 Te 3 /FeTe topological insulator-chalcogenide interface superconductor at temperatures well below the Berezinski-Kosterlitz-Thouless transition. We observe a transition in the current-resistance and temperature-resistance curves that quantitatively agrees with the Likharev vortex-explosion phenomenon. In the limit of low temperatures and high current densities, we were able to demonstrate the regime of complete vortex-antivortex dissociation arising from current driven vortex-antivortex pair breaking. [ABSTRACT FROM AUTHOR]

The linearized Usadel equations in a generalized form containing both the spin singlet and the odd frequency spin triplet pair amplitudes in an s-wave state are used to study the oscillatory behavior of the superconducting critical temperature T c due to the influence of an external magnetic field in proximity coaxial cylinders of a ferromagnetic core surrounded by a superconducting shell. Such geometry modifies the pairing wavefunction periodically with the vortex number L . The exchange field in the ferromagnetic core is chosen to be of the spiral type which rotates in the plane with a spiral wave vector Q . The external magnetic field assumes a constant value and is directed perpendicularly to the plane. The switching phenomena of the induced superconductivity in the ferromagnet with various vortex numbers are investigated in detail by solving self-consistently the Usadel equations to determine the Little–Parks effect i.e., the behavior of T c versus a magnetic flux threading the ferromagnetic core. [ABSTRACT FROM AUTHOR]

Insulating columnar inclusions in a type II chiral $$p_x \pm i p_y$$ superconductor are shown to affect essentially the electronic structure of pinned vortices, and, as a consequence, the scanning tunneling microscopy (STM) patterns and the microwave response in the vortex phase. The structure of the anomalous spectral branch analyzed within the Bogolubov-de Gennes theory is found to depend strongly on the mutual orientation of the angular momenta of the center of mass and the relative motion of two electrons in the Cooper pair. This dependence reveals itself in the nontrivial behavior of the Hall part of the microwave response and difference of the STM patterns for opposite magnetic field orientations. [ABSTRACT FROM AUTHOR]

The time-dependent Ginzburg-Landau equations have been solved numerically by the finite-element method for a three-dimensional mesoscopic superconducting torus. We obtain the different vortex patterns as a function of the applied field perpendicular to its surface. And we find that multivortex states are ground state in a three-dimensional mesoscopic torus. These results show that our approach is effective and useful to interpret experimental data on vortex states in mesoscopic superconductors. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The time-dependent Ginzburg-Landau equations have been solved numerically by a finite element analysis for the nanosized superconducting strips with one central weak link. Anisotropy is included through the spatially dependent anisotropy coefficient ζ in different layers of the sample. For given applied magnetic fields, we have simulated the dynamical behavior of the penetrating magnetic vortices into the superconductor. Our results show the energy barrier for vortices to enter a weak link is smaller than that for vortices to enter superconducting layers. The final distribution of vortices is determined by the competing interactions of vortices with Meissner currents and the weak link boundaries. [ABSTRACT FROM AUTHOR]

We theoretically investigate the local magnetic field, order parameter and supercurrent profiles of a parallelepiped mesoscopic superconductor submersed in an applied magnetic field; this same geometry with a pillar on its top surface is also considered. Our investigation was carried out by solving the three-dimensional time-dependent Ginzburg–Landau (TDGL) equations. We obtain the magnetization curve as a function of the external applied magnetic field for several sample sizes. We have determined an analytical dependence of the thermodynamic fields and the magnetization as functions of the lateral dimension of the superconductor. Finally, a systematic comparative study of the two- and three-dimensional approaches of the Ginzburg–Landau model is carried out. [ABSTRACT FROM AUTHOR]

Using the nonlinear Ginzburg–Landau equations we study the vortex configurations in a superconducting square with a central square pillar in the presence of a uniform applied magnetic field. The presence of the pillar changes the vortex structure in the superconducting sample considerably. We calculate magnetization, magnetic induction, supercurrent and vorticity, which show different vortex configurations as a function of magnetic field. [ABSTRACT FROM AUTHOR]

In order to study site-selective NMR in chiral p -wave superconductors, we calculate local nuclear relaxation rate T 1 − 1 in the vortex lattice state by Eilenberger theory with and without non-magnetic impurity scattering in the Born limit and unitary limit. The local T 1 − 1 in the NMR resonance line shape is different between two chiral states p ± , depending on whether the chirality is parallel or anti-parallel to the vorticity. In the p − -wave, anomalous suppression of local T 1 − 1 occurs around the vortex core due to the negative coherence term coming from odd-frequency s -wave Cooper pair induced around the vortex. We especially examine the site dependence of the anomalous suppression of local T 1 − 1 , including the applied magnetic field dependence and the impurity effects. [ABSTRACT FROM AUTHOR]

The resistive state of a superconductor in magnetic field has been thoroughly investigated both by experiments and by theoretical simulations. However, a local study of vortex dynamics inducing dissipation was performed only recently by means of scanning Hall probe microscopy (SHPM). In this work we extend this idea and we visualize the oscillatory motion of vortices in NbSe2 using scanning tunneling microscopy (STM). In contrast to previous experiments, sensitive to magnetic fields, the STM probes the local density of states and the local topography. Its ability to resolve vortices is limited by the coherence length. In the case of type-II superconductors this is expected to resolve vortex motion beyond the detection limit of the SHPM. We experimentally verify the enhanced sensitivity by observing vortex motion in a very dense vortex lattice (H=600mT). [ABSTRACT FROM AUTHOR]

In this work we solved the time-dependent Ginzburg-Landau equations, TDGL, to simulate two superconducting systems with different lateral sizes and with an antidot inserted in the center. Then, by cycling the external magnetic field, the creation and annihilation dynamics of a vortex-antivortex pair was studied as well as the range of temperatures for which such processes could occur. We verified that in the annihilation process both vortex and antivortex acquire an elongated format while an accelerated motion takes place. [ABSTRACT FROM AUTHOR]

The time-dependent Ginzburg-Landau equations have been solved numerically by a finite-element analysis for a mesoscopic superconducting square structure with four nanoscale holes in two-dimensional space. For given applied magnetic fields we have simulated the dynamical behavior of the penetrating magnetic vortices into the superconductor. Our results show that the mesoscopic superconductor can be tuned to exhibit the clear separation of the multivortex by properly introducing the nanoscale holes in a mesoscopic superconductor. [ABSTRACT FROM AUTHOR]

We study the effects of non-magnetic impurity scattering on the Andreev bound states (ABS) in an isolated vortex in two-dimensional chiral p-wave superconductors numerically. We incorporate the impurity scattering effects into the quasiclassical Eilenberger formulation through the self-consistent t-matrix approximation. Within this scheme, we calculate the local density of states (LDOS) around two types of vortices: 'parallel' ('anti-parallel') vortex where the phase winding of the pair-potential coming from the vorticity and that coming from the chirality have the same (opposite) sign. When the scattering phase-shift δ of each impurity is small, we find that the impurities affect differently the spectra of quasiparticles localized around the two types of vortices in a way similar to that in the Born limit ( δ→0). For a larger δ(≲ π/2), ABS in the vortex is strongly suppressed by the impurities for both types of vortices. We find that there are some correlations between the suppression of ABS near vortex cores and the low energy density of states due to the impurity bands in the bulk. [ABSTRACT FROM AUTHOR]

Highlights: [•] We study the switching phenomena in hybrid SC/FM coaxial cylinders. [•] The s-wave triplet Usadel equations are considered. [•] We investigate the T c behavior with different vorticities. [•] Numerical results exhibit the vortex states in favor of superconductivity in FM. [Copyright &y& Elsevier]

Highlights: [•] Using the Ginzburg–Landau equation, vortex structures in a pentagonal plate superconductor are investigated. [•] Structures of vortices break a fivefold rotational symmetry. [•] Distribution of amplitude of the order parameter breaks a fivefold rotational symmetry. [ABSTRACT FROM AUTHOR]

Abstract: The influence of superficial defects on the vortex configurations of a thin superconducting disk is investigated within the time dependent Ginzburg–Landau formalism. The free energy, magnetization, vorticity, and the Cooper pair density are calculated for both metastable and stable vortex configurations and different number of defects on its surface in the presence of an external magnetic field applied perpendicular to the disk area. We show that the competition between the confinement geometry and the geometric position of the defects leads to non-conventional vortex configurations which are not compatible with the symmetry of the sample geometry. [Copyright &y& Elsevier]

Using electron holography and coherent beam Lorentz microscopy, Akira Tonomura investigated the physics of magnetic flux lines, or vortices, in metal and high-temperature superconductors for more than 20 years. The methodology he developed for doing this made use of coherent electron waves from cold-emission (field-emission) sources and their quantum–mechanical phase shifts. Using 300-kV and 1-MV electron microscopes, Tonomura and his team clarified the dynamic behavior of magnetic flux lines in Pb and Nb superconductors and in high-temperature \YBa2\Cu3\O7-\delta and \Bi2\Sr2\CaCu2\O8 + \delta superconductors. This memorial paper reviews the static and dynamic flux-line behaviors in superconductors as revealed by their results. [ABSTRACT FROM PUBLISHER]

Abstract: We study the vortex profiles in two-gap superconductors using the extended Ginzburg–Landau theory. The results shed more light on the disparity between the effective length scales in two bands. We compare the behavior expected from the standard Ginzburg–Landau theory with this new approach, and find good qualitative agreement in the case of LiFeAs. [Copyright &y& Elsevier]

One of the important performance parameters of superconducting nanowire single photon detectors (SNSPD) is the dark count rate. Dark counts are related to thermally-activated hopping of magnetic vortices across the nanowire. We present an experimental analysis of how the thermal coupling of the NbN SNSPD to the heat sink affects the dark count rate. It was found that the rate decreases with the increase in coupling strength while the detection efficiency remains almost constant. [ABSTRACT FROM AUTHOR]

Vortices (magnetic flux quanta) in the superconducting networks perforated with anti-dots (holes) arrays behave as electrons in atomic lattice of crystals. Repulsive and attractive interaction among vortices and anti-dots resemble to those among electrons and atoms in crystals. To confirm the variety of the vortex physics similar to the solid state physics, we have fabricated such superconducting networks with antidots array in metallic, inter-metallic and high- T superconductors (HTSCs), and have measured magneto-resistance of vortex-flow. In these materials, we have observed integer-matching at the matching fields and fractional-matching effect between them. Most of them are well explained by commensurability between Abrikosov vortex lattice and anti-dots array. Furthermore, the effect of the anti-dots array in HTSCs appears as another kind of phase transitions instead of to the first-order melting transition of vortex lattice in pristine samples. [ABSTRACT FROM AUTHOR]

Abstract: We investigate non-trivial localized solutions of the condensate in a ()-dimensional D-wave holographic superconductor model in the presence of a background magnetic field. The calculation is done in the context of the ()-dimensional dual gravity theory of a charged massive spin-2 field in an AdS black hole background. By using numeric techniques, we find both vortex and droplet solutions. These solutions are important for studying the full phase diagram of D-wave superconductors. [Copyright &y& Elsevier]

Abstract: To explore vortex states and their dynamics in superconductors with large thermal fluctuation and artificial pinning potentials, we have studied the influence of periodic arrays of antidots in high-T c superconductor Bi2Sr2CaCu2O8+y (Bi2212). The diameter dependence of the matching effect in Bi2212 without a change of the thickness and oxygen doping level was investigated using one Bi2212 single-crystal film of homogeneous thickness in which several different-diameter antidot arrays were introduced. The matching effect observed by vortex-flow resistance measurements changed systematically depending on the diameter. The antidot-diameter dependence of the irreversibility lines was examined. [Copyright &y& Elsevier]

Abstract: We investigate the situation where a mesoscopic 1D ring or 2D cylinder is subject to a magnetic field by simulating the time dependant Ginzburg–Landau equations with periodic boundary conditions. We investigate the different possible evolutions for the 1D phase slip phenomenon. The case of the multiple phase slips is analyzed in details and we study the competition between simultaneous and consecutive multiple phase slips analytically and numerically. In 2D we study the creation of vortex–antivortex pairs. Following the theory of the Kibble–Zurek mechanism, we quenched the sample by applying a strong current and observe vortex–antivortex pairs dynamics. [ABSTRACT FROM AUTHOR]

We summarize some results on the behavior of vortex dynamics and pinning effects in superconducting films with artificial pinning centers. Superconducting thin films with regular arrays of holes were fabricated using electron-beam lithography and reactive dry etching techniques. Vortex dynamics in the mixed state in type II superconductors is strongly influenced by the presence of defects, which act as pinning centers. Periodic critical current matching peaks were observed in magnetotransport measurements. The matching effect is caused by the interplay between the pinning centers and vortex lattice. Therefore, vortex lattice behaviors are changed for different temperatures and the geometry of the pinning centers. Molecular dynamic simulations are made to study this phenomenon. The ground state distribution of vortices obtained from simulations can give a reasonable explanation of the prominent matching peaks we found in the experiments. [ABSTRACT FROM AUTHOR]

Results of modeling of superconductor magnetization process based on a numerical solution of the timedependent Ginsburg-Landau equations are presented. Methods of grid approximation of the equations and method of finite elements are used. Two-dimensional patterns of changes in the order parameter and supercurrent distribution in superconductors are calculated and visualized. The main results are in agreement with the well-known representations for type I and II superconductors. [ABSTRACT FROM AUTHOR]

Abstract: This short review aims to summarize on “what the charge density waves can tell to other inhomogeneous states in strongly correlated systems, particularly to spin-polarized superconductors”. We shall update on expanding observations of solitons in quasi 1D CDW conductors and link them to the growing information and demands related to inhomogeneous spin-polarized states in superconductors. The related theory, existent or awaited for, stretches from solitons in 1D models to vortex-like elementary excitations in 2D, 3D ordered incommensurate CDWs and superconductors. [Copyright &y& Elsevier]

We have investigated the behavior of vortices in a polycrystalline YBa2Cu3O7-δ disk sample using rotational magnetization-vector (RMV) measurements. The measurements were conducted in the field-cooled (FC) and the zero-field cooled (ZFC) states for several values of applied magnetic field parallel to the sample surface at 4.2 K and for various angles of rotation (θrot) up to 360°. The total magnetic flux density, B, in the sample at any rotational angle was considered to be composed of two types of vortices: weakly pinned vortices that rotate frictionally in the opposite direction of sample rotation and strongly pinned vortices that rotate rigidly in the same direction of sample rotation. From the rate of change of these two types of vortices and the rate of change of B, we were able to develop a tool to qualitatively describe the average strength of pinning centers in high-temperature superconductors. [ABSTRACT FROM AUTHOR]

Abstract: Vortex states in a Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superconductor are microscopically investigated by the quasi-classical Eilenberger theory. We calculate the spatial structure of the pair potential, paramagnetic magnetization (i.e., Knight shift in a magnetic field) and electronic states, including paramagnetic depairing effect in addition to the orbital depairing effect. Topologies of 2π phase winding at the vortex line and π phase shift at the FFLO nodal plane affect the distribution of paramagnetic magnetization and low energy electronic states. We also discuss the NMR resonance line shape observed in the high field phase of CeCoIn5. [Copyright &y& Elsevier]

Abstract: Local magnetic images of electron-doped Nd2−x Ce x CuO4 (NCCO) superconducting single crystals above and below the critical temperature T c were obtained using scanning superconducting quantum interference device (SQUID) microscopy. Surface scanning of the ab-plane of an NCCO (x =0.15) crystal cooled to 3K under a low magnetic field (∼1μT) revealed vortex patterns clearly. These vortex patterns totally disappeared at temperatures higher than T c. In contrast, when the crystal is cooled below T c under an external magnetic field (i.e., additional magnetic field controlled by a coil or plating sample stage), an unusual ‘stripe-shaped’ magnetic image is observed due to alignment of the vortices in a quasi-1D manner. [Copyright &y& Elsevier]

The effect of fractal clusters on magnetic and transport properties of percolative superconductors is studied. The superconductor contains percolative superconducting cluster carrying a transport current and clusters of a normal phase. It is found that normal phase clusters have essential fractal features. The fractal dimension of the boundary of normal phase clusters is estimated. The current-voltage (V — I) characteristics of superconductors containing fractal clusters are obtained. It is found that the fractality of the cluster boundary intensifies pinning. This feature permits to enhance the current-carrying capability of the superconductors. [ABSTRACT FROM AUTHOR]

Abstract: In the present work we investigate the behavior of a vortex in a long superconducting cylinder near to a columnar defect at the center. The derivations of the local magnetic field distribution and the Gibbs free energy will be carried out for a cylinder and a cavity of arbitrary sizes. From the general expressions, it is considered two particular limits: one in which the radius of the cavity is very small but the radius of the superconducting cylinder is kept finite; and one in which the radius of the superconducting cylinder is taken very large (infinite) but the radius of the cavity is kept finite. In both cases the maximum number of vortices which are allowed in the cavity is determined. In addition, the surface barrier field for flux entrance into the cavity is calculated. [Copyright &y& Elsevier]

A rigid ferromagnetic ground state, formed by a rectangular array of magnetic moments, is embedded in a superconductor. Insulating spheres are pinning centers with magnetic moment, and their interaction with the vortex matter is described here through a Ginzburg–Landau theory that treats superconducting and insulating regions on the same footing. For a critical value of the magnetic moment vortices undergo a deconfinement transition giving rise to a collective state of vortices and anti-vortices. [Copyright &y& Elsevier]

The current-driven three-dimensional frustrated anisotropic XY model with strong disorder is simulated to model the moving vortex matter in layered superconductors. The equilibrium disordered state can be driven to a moving Bragg glass (BrG) by applying an external current. As the pinning strength increases, the moving BrG can melt into a moving smectic via a first-order phase transition. [ABSTRACT FROM AUTHOR]

We investigated the paramagnetic supercurrent and the transition points between different vortex states in mesoscopic superconducting disks. We observed paramagnetic supercurrent in four disks: two 33 nm thick and two 50 nm thick, all 1.50 μm in diameter. Analyses of the supercurrent symmetry and the intervals between transition points showed that defects did not play a crucial role in our samples or in the samples first reported to show the paramagnetic Meissner effect (PME) [Nature 396 (1998) 144]. This supports our previous conclusion that the origin of the PME is the paramagnetic supercurrent. [Copyright &y& Elsevier]

A single vortex in the charged Bose-gas (CBG) has a charged core and its profile different from the vortex in neutral and BCS superfluids. Lower and upper critical fields of CBG are discussed. The unusual resistive upper critical field, Hc2(T), of many cuprates and a few other unconventional superconductors is described as the Bose–Einstein condensation field of preformed bosons–bipolarons. Its nonlinear temperature dependence follows from the scaling arguments. Exceeding the Pauli paramagnetic limit is explained. Controversy in the determination of Hc2(T) of cuprates from kinetic and thermodynamic measurements is addressed in the framework of the bipolaron theory. [Copyright &y& Elsevier]

The superconducting state of mesoscopic square samples with two and four antidots is studied using the nonlinear Ginzburg–Landau (GL) theory. We found a qualitative difference in the nucleation of the superconducting state in samples with different number of antidots, which is related to the interplay of the different types of symmetry. The H–T phase diagram of these structures reveals an oscillatory behavior caused by the formation of different stable vortex configurations in these small clusters of pinning centers. A comparison with the experiment of H–T phase diagram is given. [Copyright &y& Elsevier]

We prepared a sample of a square microhole lattice by evaporating a type-I superconductor lead on a copper micromesh sieve with 16.9-μm pitch. We explore the superconducting properties using a superconducting quantum interference device magnetization measurement. We found the anomalous matching effect in the magnetization curve where the matching peaks have the same polarity in both positive and negative field branches. The positive magnetization appears upon field cooling either in positive or negative field. The magnetization appears even upon cooling in zero fields. This might be a manifestation of spontaneous magnetization like a ferromagnetic substance. It was pointed out that the vortex current reversal occurs for a superconductor of a Ginzburg–Landau parameter κ∼1. This is the origin of the attractive vortex–vortex interaction. We consider that the attractive interaction plays a major role in forming spontaneous vortex domains. [Copyright &y& Elsevier]

In Magnet/Superconductor Nanostructures it is possible to control magnetism and conductivity at the nanoscale by using localized magnetic fields from structural (dots, stripes, wires) and topological (vortices's, skyrmions and domain walls) textures in magnet and/or superconductor subsystems of the hybrid material. We review experimental and theoretical results in the field of nanostructured magnet/superconductor systems. [ABSTRACT FROM AUTHOR]