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"

Hall potentiometer in the ballistic regime

We demonstrate theoretically how a two-dimensional electron gas can be used to probe local potential profiles using the Hall effect. For small magnetic fields, the Hall resistance is inversely proportional to the average potential profile in the Hall cross and is independent of the shape and the position of this profile in the junction. The bend resistance, on the other hand, is much more sensitive on the exact details of the local potential profile in the cross junction.Comment: 3 pages, 4 ps figure

Saddle point states and energy barriers for vortex entrance and exit in superconducting disks and rings

The transitions between the different vortex states of thin mesoscopic superconducting disks and rings are studied using the non-linear Ginzburg-Landau functional. They are saddle points of the free energy representing the energy barrier which has to be overcome for transition between the different vortex states. In small superconducting disks and rings the saddle point state between two giant vortex states, and in larger systems the saddle point state between a multivortex state and a giant vortex state and between two multivortex states is obtained. The shape and the height of the nucleation barrier is investigated for different disk and ring configurations.Comment: 10 pages, 18 figure

From vortex molecules to the Abrikosov lattice in thin mesoscopic superconducting disks

Stable vortex states are studied in large superconducting thin disks (for numerical purposes we considered with radius R = 50 \xi). Configurations containing more than 700 vortices were obtained using two different approaches: the nonlinear Ginzburg-Landau (GL) theory and the London approximation. To obtain better agreement with results from the GL theory we generalized the London theory by including the spatial variation of the order parameter following Clem's ansatz. We find that configurations calculated in the London limit are also stable within the Ginzburg-Landau theory for up to ~ 230 vortices. For large values of the vorticity (typically, L > 100), the vortices are arranged in an Abrikosov lattice in the center of the disk, which is surrounded by at least two circular shells of vortices. A Voronoi construction is used to identify the defects present in the ground state vortex configurations. Such defects cluster near the edge of the disk, but for large L also grain boundaries are found which extend up to the center of the disk.Comment: 15 pages, 10 figures, RevTex4, submitted to Phys. Rev.

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 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.