Magnetic coupling between mesoscopic superconducting rings

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.Comment: 3 pages text, 3 ps figures, to be published in Physica C (Proceedings of the 2nd European Conference in School Format "Vortex Matter in Superconductors"

Stationary phase slip state in quasi-one-dimensional rings

The nonuniform superconducting state in a ring in which the order parameter vanishing at one point is studied. This state is characterized by a jump of the phase by $\pi$ at the point where the order parameter becomes zero. In uniform rings such a state is a saddle-point state and consequently unstable. However, for non-uniform rings with e.g. variations of geometrical or physical parameters or with attached wires this state can be stabilized and may be realized experimentally.Comment: 6 pages, 7 figures, RevTex 4.0 styl

Dynamics of the superconducting condensate in the presence of a magnetic field. Channelling of vortices in superconducting strips at high currents

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 ($J_{c2}$ \cite{self1}) 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 $J_{c1}=J_{c2}=J_c$. In this high magnetic field region and for currents close to $J_c$ 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.Comment: 5 pages, 4 figures, Proceedings of Third European Conference on Vortex Matter in Superconductor

Superconducting thin rings with finite penetration depth

Recently Babaei Brojeny and Clem [Phys. Rev. B 68, 174514 (2003)] considered superconducting thin-film rings in perpendicular magnetic fields in the ideal Meissner state with negligibly small magnetic penetration depth and presented useful analytical limiting expressions and numerical results for the magnetic-field and sheet-current profiles, trapped magnetic flux, self-inductance, magnetic moment, and focusing of magnetic flux into the hole when no net current flows in the ring. The present paper generalizes all these results to rings with arbitrary values of the two-dimensional effective penetration depth \Lambda = \lambda^2 /d (\lambda is the London depth and d < \lambda/2 the film thickness) using a straightforward matrix inversion method. We also present results for the energy of a superconducting ring as a function of the applied magnetic induction B_a and the quantum number N defining the size of the fluxoid N \phi_0 trapped in the hole.Comment: with 19 figures, gives 11.5 page

Properties of mesoscopic superconducting thin-film rings. London approach

Superconducting thin-film rings smaller than the film penetration depth (the Pearl length) are considered. The current distribution, magnetic moment, and thermodynamic potential ${\cal F}(H,N,v)$ for a flat, washer-shaped annular ring in a uniform applied field $H$ perpendicular to the film are solved analytically within the London approach for a state with winding number $N$ and a vortex at radius $v$ between the inner and outer radii.Comment: Submitted to Phys. Rev.

Superconducting properties of mesoscopic cylinders with enhanced surface superconductivity

The superconducting state of an infinitely long superconducting cylinder surrounded by a medium which enhances its superconductivity near the boundary is studied within the nonlinear Ginzburg-Landau theory. This enhancement can be due to the proximity of another superconductor or due to surface treatment. Quantities like the free energy, the magnetization and the Cooper-pair density are calculated. Phase diagrams are obtained to investigate how the critical field and the critical temperature depend on this surface enhancement for different values of the Ginzburg-Landau parameter \kappa. Increasing the superconductivity near the surface leads to higher critical fields and critical temperatures. For small cylinder diameters only giant vortex states nucleate, while for larger cylinders multivortices can nucleate. The stability of these multivortex states also depends on the surface enhancement. For type-I superconductors we found the remarkable result that for a range of values of the surface extrapolation length the superconductor can transit from the Meissner state into superconducting states with vorticity L > 1. Such a behaviour is not found for the case of large \kappa, i.e. type-II superconductivity.Comment: submitted to Phys. Rev.

Dependence of the vortex configuration on the geometry of mesoscopic flat samples

The influence of the geometry of a thin superconducting sample on the penetration of the magnetic field lines and the arrangement of vortices are investigated theoretically. We compare superconducting disks, squares and triangles with the same surface area having nonzero thickness. The coupled nonlinear Ginzburg-Landau equations are solved self-consistently and the important demagnetization effects are taken into account. We calculate and compare quantities like the free energy, the magnetization, the Cooper-pair density, the magnetic field distribution and the superconducting current density for the three geometries. For given vorticity the vortex lattice is different for the three geometries, i.e. it tries to adapt to the geometry of the sample. This also influences the stability range of the different vortex states. For certain magnetic field ranges we found a coexistence of a giant vortex placed in the center and single vortices toward the corners of the sample. Also the H-T phase diagram is obtained.Comment: 9 pages, 17 figures (submitted to Phys. Rev. B

Vortex Matter in Mesoscopic Superconducting Disks and Rings

Phase transitions between different (i.e. giant and multi-vortex) superconducting states and between the superconducting-normal state of mesoscopic disks and rings are studied in the presence of an external magnetic field by solving the two non-linear Ginzburg-Landau equations self-consistently. The flux through a circular disk with a hole in the middle is not quantized.Comment: 8 pages, 10 figures; to appear in Physica C (proceedings of the conference on Vortex matter, Crete (september 1999

Flux transitions in a superconducting ring

We perform a numeric study of the flux transitions in a superconducting ring at fixed temperature, while the applied field is swept at an ideally slow rate. The current around the ring and its free energy are evaluated. We partially explain some of the known experimental features, and predict a considerably large new feature: in the vicinity of a critical field, giant jumps are expected