Nucleation of Superconductivity in a Mesoscopic Loop of Finite Width

The normal/superconducting phase boundary Tc has been calculated for mesoscopic loops, as a function of an applied perpendicular magnetic field H. While for thin-wire loops and filled disks the Tc(H) curves are well known, the intermediate case, namely mesoscopic loops of finite wire width, have been studied much less. The linearized first Ginzburg-Landau equation is solved with the proper normal/vacuum boundary conditions both at the internal and at the external loop radius. For thin-wire loops the Tc(H) oscillations are perfectly periodic, and the Tc(H) background is parabolic (this is the usual Little-Parks effect). For loops of thicker wire width, there is a crossover magnetic field above which Tc(H) becomes quasi-linear, with the period identical to the Tc(H) of a filled disk (i.e. pseudoperiodic oscillations). This dimensional transition is similar to the 2D-3D transition for thin films in a parallel field, where vortices start penetrating the material as soon as the film thickness exceeds the temperature dependent coherence length by a factor 1.8. For the presently studied loops, the crossover point is controlled by a similar condition. In the high field '3D' regime, a giant vortex state establishes, where only a surface superconducting sheath near the sample's outer radius is present.Comment: 7 pages text, 2 EPS figures, uses LaTeX's elsart.sty, proceedings of the First Euroconference on "Vortex Matter in Superconductors", held in Crete (18-24 september 1999

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"

Confinement and Quantization Effects in Mesoscopic Superconducting Structures

We have studied quantization and confinement effects in nanostructured superconductors. Three different types of nanostructured samples were investigated: individual structures (line, loop, dot), 1-dimensional (1D) clusters of loops and 2D clusters of antidots, and finally large lattices of antidots. Hereby, a crossover from individual elementary "plaquettes", via clusters, to huge arrays of these elements, is realized. The main idea of our study was to vary the boundary conditions for confinement of the superconducting condensate by taking samples of different topology and, through that, modifying the lowest Landau level E_LLL(H). Since the critical temperature versus applied magnetic field T_c(H) is, in fact, E_LLL(H) measured in temperature units, it is varied as well when the sample topology is changed through nanostructuring. We demonstrate that in all studied nanostructured superconductors the shape of the T_c(H) phase boundary is determined by the confinement topology in a unique way.Comment: 28 pages, 19 EPS figures, uses LaTeX's aipproc.sty, contribution to Euroschool on "Superconductivity in Networks and Mesoscopic Systems", held in Siena, Italy (8-20 september 1997

Superconductivity in a Mesoscopic Double Square Loop: Effect of Imperfections

We have generalized the network approach to include the effects of short-range imperfections in order to analyze recent experiments on mesoscopic superconducting double loops. The presence of weakly scattering imperfections causes gaps in the phase boundary $B(T)$ or $\Phi(T)$ for certain intervals of $T$, which depend on the magnetic flux penetrating each loop. This is accompanied by a critical temperature $T_c(\Phi)$, showing a smooth transition between symmetric and antisymmetric states. When the scattering strength of imperfections increases beyond a certain limit, gaps in the phase boundary $T_c(B)$ or $T_c(\Phi)$ appear for values of magnetic flux lying in intervals around half-integer $\Phi_0=hc/2e$. The critical temperature corresponding to these values of magnetic flux is determined mainly by imperfections in the central branch. The calculated phase boundary is in good agreement with experiment.Comment: 9 pages, 6 figure

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

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

Giant vortex state in perforated aluminum microsquares

We investigate the nucleation of superconductivity in a uniform perpendicular magnetic field H in aluminum microsquares containing a few (2 and 4) submicron holes (antidots). The normal/superconducting phase boundary T_c(H) of these structures shows a quite different behavior in low and high fields. In the low magnetic field regime fluxoid quantization around each antidot leads to oscillations in T_c(H), expected from the specific sample geometry, and reminiscent of the network behavior. In high magnetic fields, the T_c(H) boundaries of the perforated and a reference non-perforated microsquare reveal cusps at the same values of Phi/Phi_0 (where Phi is the applied flux threading the total square area and Phi_0 is the superconducting flux quantum), while the background on T_c(H) becomes quasi-linear, indicating that a giant vortex state is established. The influence of the actual geometries on T_c(H) is analyzed in the framework of the linearized Ginzburg-Landau theory.Comment: 14 pages, 6 PS figures, RevTex, accepted for publication in Phys. Rev.

Critical temperature oscillations in magnetically coupled superconducting mesoscopic loops

We study the magnetic interaction between two superconducting concentric mesoscopic Al loops, close to the superconducting/normal phase transition. The phase boundary is measured resistively for the two-loop structure as well as for a reference single loop. In both systems Little-Parks oscillations, periodic in field are observed in the critical temperature Tc versus applied magnetic field H. In the Fourier spectrum of the Tc(H) oscillations, a weak 'low frequency' response shows up, which can be attributed to the inner loop supercurrent magnetic coupling to the flux of the outer loop. The amplitude of this effect can be tuned by varying the applied transport current.Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev.