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Magnetic vortex structures in a superconductor under a helical magnetic field are investigated using the Ginzburg-Landau equations and the three-dimensional finite element method. Magnetic-field-amplitude dependence of vortex structure is investigated. Also how superconductivity is destroyed is shown. Also peculiar vortex structures are found under the helical magnetic field. [ABSTRACT FROM AUTHOR]

We present direct observations of vortex configurations in Mo80Ge20 pentagonal plates using a scanning SQUID microscope. The vortex distribution tends to adapt to one of five symmetric axes in a pentagon, as expected from the sample geometry. We found that, for a vorticity of six, the vortices form a two-shell structure in a small pentagon, and a single-shell structure in a larger pentagon. We revealed how the vortex configuration is strongly modified by the presence of a pinning site at the center of the pentagon. In particular, a two-shell structure is formed in the pinning-site sample with a vorticity of L = 4, while the second shell appeared in the pinning site-free sample with a vorticity up to L = 6. Furthermore, upon geometric confinement, the vortices attempt to form a symmetrical configuration reflecting the sample geometry even in the presence of a pinning site (or sites). The experimental results for pentagons are in good agreement with our theoretical predictions based on the nonlinear Ginzburg-Landau equation both for a pin-free pentagon and a pentagon with a pin at the center. [ABSTRACT FROM AUTHOR]

In this review, we describe finite superconducting networks which consist of mutually connected superconducting wires. These are two-dimensional square and honeycomb networks and three-dimensional tetrahedron, octahedron and C60 networks. Because of multi-connectivity, they show a wide variety of magnetic flux structures under an external magnetic field. Also we show the effect of disorder on the flux structures and the penetration dynamics of the fluxons. [ABSTRACT FROM AUTHOR]

Abstract: We consider superconducting states of a nano-sized two-band superconductor, where one of the bands is a hole band and anotherisan electron band.We formulatethe microscopic numerical methodfortwo-band superconductorsusing the Bogoliubov-de Gennes equation and the finite element method. We show the several vortex structures under an external field. [Copyright &y& Elsevier]

Abstract: We have developed numerical simulation method for quasi-particle structures in the three-dimensional nano-sized superconductors, using the three-dimensional finite element method and the Bogoliubov-de Gennes equation. Using this method, we analyzed the superconducting state in the nano-sized cubic superconductors. We found the spatial oscillations of order parameter because of the confinement of superconducting electrons, and also we found the quasi-particle bound states at the corners of the cubic superconductors because of suppression of superconductivity at the corners. [Copyright &y& Elsevier]

We solved the Ginzburg–Landau (GL) equation for several superconducting networks. First, using de Gennes–Alexander (dGA) approach, we solved linearized GL equation for the buckminsterfullerene network and obtained magnetic field dependence of superconducting transition temperature and fluxoid patterns. Second, we solved GL equation for square lattices. Magnetic field dependence of superconducting transition temperature was calculated by the dGA network equation and also spatial distribution of the order parameter was calculated by the finite-element method for the GL equation. [Copyright &y& Elsevier]

Abstract: Using the de Gennes–Alexander equation, we have investigated the stable vortex structures in finite superconducting networks (10×10 holes) with disordered wires under an external magnetic field. Vortex structures change gradually with increasing magnetic field. For the network with a disordered wire at the edge, vortices are not pinned disordered hole, but enter into the network at the holes with the disorder. But for the network with two disordered wires, the vortex enters at the hole between two disordered wires. This behavior can be considered as the result of the nonlocality of superconductivity. [ABSTRACT FROM AUTHOR]

Abstract: Nanoscopic superconductors have several properties that are different from bulk superconductors. However, only symmetric s-wave superconductors have been investigated. In order to investigate novel states microscopically, we have solved Bogoliubov–de Gennes equation for nanoscopic d-wave superconductors. The result shows that the node states are modified in the nanoscopic plate. [Copyright &y& Elsevier]

Abstract: Using the Bogoliubov–de Gennes equation on the tight-binding electron model, we have investigated nano-structured anisotropic superconductors. For a π/4-rotated square d-wave superconducting plate, the superconducting symmetry becomes s+id, not only at the surfaces, but over the whole superconductor. Also we have investigated quasi-particle structures of this superconducting state. [Copyright &y& Elsevier]

Abstract: Using the Bogoliubov-de Gennes equation of a tight-binding electron model with attractive on-site and nearest-neighbor sites interactions, we investigate the superconducting structure of nano-structured anisotropic superconductors. Numerical results show that nano-scaled π/4-rotated square d-wave superconductors show various type of superconductivities depending on the size. Especially, s+id superconductivity, appears when size of superconductors is 10 times of coherence length. [Copyright &y& Elsevier]

Superconducting finite-sized Pb square networks with 10×10 square holes fabricated by electron beam lithography have been investigated in view of vortex doping into superconducting networks. Vortex images observed by a SQUID microscope were compared with predictions from the Ginzburg-Landau theory. Exactly reversed pattern was confirmed to appear both in the vortex-doping x into an empty network and in the antivortex doping 1-x into a fully occupied network (x=1/4). We also confirmed a checker-board crystal of vortices at half filling both theoretically and experimentally. [ABSTRACT FROM AUTHOR]

Abstract: We report theoretical results of vortex configurations, and critical fields of regular square micro-plates with 2×2 anti-dots by using the Ginzburg–Landau theory. To treat inhomogeneousness of the system, we applied the finite element method (FEM). We have calculated the Gibbs free energies for two types of plates with different anti-dots sizes. We found that 0Φ 0 and 4Φ 0 vortex states are extremely stable states. [Copyright &y& Elsevier]

We have found the self-consistent solution of Bogoliubov-de Gennes equation for a single vortex in d-wave superconductors. Unlike earlier studies, we consider the more realistic case pFξ=10, where pF is the Fermi momentum and ξ0=vF/Δ is the coherence length. Here we present the temperature dependence of the vortex core radius and the spatial dependence of the relaxation time T1 of NMR. Also we discuss the pFξ dependence of these quantities. [Copyright &y& Elsevier]

Abstract: Using the de Gennes–Alexander equation, we have analyzed the vortex structures in disordered finite superconducting networks under an external magnetic field. The vortex structure at the superconducting transition temperature is much different from that of the regular networks. As increasing the magnetic field, the equilibrium magnetic structure changes gradually, and the disordered wires affect the position of the vortices apart from that wire. This is the non-local effect of the superconductivity. [ABSTRACT FROM AUTHOR]

Abstract: When a superconductor in the normal state is rapidly quenched into the superconducting state, vortices are formed spontaneously if the Kibble–Zurek scenario works in the superconducting transition. We perform numerical simulations for the relaxation of quenched superconducting films with and without micro-holes. It is shown that the use of type-I superconducting films with micro-holes is promising for the detection of the spontaneous vortices induced by quenching. [Copyright &y& Elsevier]

Abstract: In order to examine a potentiality of an MgB2 narrow strip as a neutron detector, we perform numerical simulations on non-equilibrium superconducting dynamics by solving the time-dependent Ginzburg–Landau equation coupled with the Maxwell and the heat diffusion equations. The simulation reveals a time period of the electrical response associated with the non-equilibrium superconducting dynamics after a neutron is captured on the top surface of the MgB2 strip. [Copyright &y& Elsevier]

We investigated vortex states in small star-shaped Mo 80 Ge 20 plates both theoretically and experimentally. The numerical calculations of the Ginzburg–Landau equation have been carried out with the aid of the finite element method, which is convenient to treat an arbitrarily shaped superconductor. The experimental results were observed by using a scanning SQUID microscope. Through systematic measurements, we figured out how vortices form symmetric configuration with increasing the magnetic field. The vortex distribution tends to adapt to one of five mirror symmetric lines when vortices were located at the five triangular horns of a star-shaped plate. The crystalline homogeneity of a sample was confirmed by the X-ray diffraction and the superconducting properties so that vortices are easily able to move for accommodating vortices in the geometric symmetry of the star-shaped plate. The experimental vortex configurations obtained for a star-shaped plate are in good agreement with theoretical predictions from the nonlinear Ginzburg–Landau equation. [ABSTRACT FROM AUTHOR]

Abstract: The extended Little–Parks effect of superconducting network is known as a periodic T c variation as a function of magnetic field. Superconducting Pb honeycomb networks of matching field 0.106G and triangular microhole lattice of Pb of matching field 0.425G have been fabricated by the combination of electron-beam lithography and a lift-off process of evaporated Pb films. The application of magnetic field corresponds to the vortex filling into superconducting networks. We measured the magnetization of the networks systematically by using a SQUID magnetometer. We found that flux jump appears rather periodically as a function of magnetic field. Flux jumps may be induced by a periodic decrease of the critical current density of the network. To the authors’ knowledge, this is for the first time to observe the regular flux jumps due to the critical current modification coming from the extended Little–Parks effect of the superconducting networks. [Copyright &y& Elsevier]