Abstract: On the basis of the time-dependent Ginzburg-Landau equation we studied the dynamics of the superconducting condensate in a wide two-dimensional sample in the presence of a perpendicular magnetic field and applied current. We could identify two critical currents: the current at which the pure superconducting state becomes unstable (J(c2)(1)) and the current at which the system transits from the resistive state to the superconducting state (J(c1) < J(c2)). The current J(c2) decreases monotonically with external magnetic field, while J(c1) exhibits a maximum at H*. For sufficient large magnetic fields the hysteresis disappears and J(c1) = J(c2) = Jc. In this high magnetic field region and for currents close to Jc the voltage appears as a result of the motion of separate vortices. With increasing current the moving vortices form,channels' with suppressed order parameter along which the vortices can move very fast. This leads to a sharp increase of the voltage. These 'channels' resemble in some respect the phase slip lines which occur at zero magnetic field. (C) 2004 Elsevier B.V. All rights reserved.

Abstract: Here we summarize results from our study of the critical depinning current J(c) versus the applied magnetic flux Phi, for: (i) quasiperiodic (QP) one-dimensional (1D) chains and (ii) 2D arrays of pinning centers placed on the nodes of a five-fold Penrose lattice. In 1D QP chains, the peaks in J(c)(Phi) are determined by a sequence of harmonics of the long and short segments of the chain. The critical current J(c)(Phi) has a remarkable self-similarity. In 2D QP pinning arrays, we predict analytically and numerically the main features of J(c)(Phi), and demonstrate that the Penrose lattice of pinning sites provides an enormous enhancement of J(c)(Phi), even compared to triangular and random pinning site arrays. This huge increase in J(c)(Phi) could be useful for applications. (c) 2005 Elsevier B.V. All rights reserved.

Abstract: The one vortex entry in a superconducting disk is investigated within the non-linear Ginzburg-Landau theory near the first critical field. We find that in mesoscopic superconducting disks the magnetic flux enters with fractions of one flux quantum phi(0) = ch/2e. For disks with a very smooth surface it is possible to drive the Meissner state so far into the metastable region that at the vortex entry a net amount of flux is expelled from the superconductor. We show that the magnetic field for flux entry is very sensitive to indentations of the disk surface and only weakly to bulges. On the other hand the flux exit field is practically insensitive to such geometrical surface defects. Our results are in agreement with recent experimental findings. (C) 2001 Elsevier Science B.V. All rights reserved.

Abstract: Transitions between different multivortex states and transitions between multivortex states and giant vortex states are observed in mesoscopic superconducting disks using the multiple-small-tunnel-junction method. These results are compared to theoretical calculations within the framework of the nonlinear Ginzburg-Landau theory. We find a good qualitative agreement between the theoretical and experimental results, when we assume that a small defect is present near the center of the experimental sample. (c) 2005 Elsevier B.V. All rights reserved.

Abstract: Using the nonlinear Ginzburg-Landau theory we investigated the dependence of the magnetic coupling between two concentric mesoscopic superconducting rings on their thickness. The size of this magnetic coupling increases with the thickness of the rings. (C) 2001 Elsevier Science B.V. All rights reserved.

Abstract: Using the two-component Ginzburg-Landau model, we investigate the effect of sample size and magnitude and homogeneity of external magnetic field on the stability of fractional vortex states in a mesoscopic two-band superconducting disk. We found that each fractional state has a preferable sample size, for which the range of applied field in which the state is stable is pronouncedly large. Vice versa, there exists an optimal magnitude of applied field for which a large range of possible sample radii will support the considered fractional state. Finally, we show that the stability of fractional states can be enhanced even further by magnetic nanostructuring of the sample, i.e. by suitably chosen geometrical parameters and magnetic moment of a ferromagnetic dot placed on top of the superconducting disk. (C) 2014 Elsevier B.V. All rights reserved.

Abstract: When a condensate is sheared by imparting a velocity to a part of the condensate, phase singularities must appear at the interface between the region that is still at rest and the region that has acquired a velocity. For helium, Feynman argued that these phase singularies will arrange themselves in the form of a vortex row. BoseEinstein condensates of ultracold atomic gases differ from helium in that the healing length is generally much larger and is, in fact, tunable. Another difference is that multicomponent condensates can be created, where the two components forming the mixture are usually two different hyperfine states of the condensed atoms. These two components can be manipulated separately and can be interconverted. In this contribution, we investigate how these additional degrees of freedom, available in quantum gases, change what happens in sheared condensates. In particular, we consider skyrmion rows as an alternative to vortex rows, and we also consider phase slip lines filled with the second, unmoving component, in a condensate mixture. We show that depending on the ratios of the interaction strengths between the components, and depending on the shear velocity, skyrmion rows and phase slip lines can become lower in energy than vortex rows, and hence should be observable in quantum gases. Moreover, we find that the velocity field affects the stability region of the condensate with respect to phase separation.

Abstract: A numerical approach to GinzburgLandau (GL) theory is demonstrated and we review its applications to several examples of current interest in the research on superconductivity. This analysis also shows the applicability of the two-dimensional approach to thin superconductors and the re-defined effective GL parameter κ. For two-gap superconductors, the conveniently written GL equations directly show that the magnetic behavior of the sample depends not just on the GL parameter of two bands, but also on the ratio of respective coherence lengths.