Abstract: Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D-2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin-Wagner-Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri-Perot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg-Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields.

Abstract: The pattern formation of the vortex states with non-monotonic inter-vortex interaction is investigated. Our applied model has a short-range repulsive (r < r(c)) and long-range attractive (r > r(c)) potential. We numerically calculate the stable states using molecular-dynamics simulations. The obtained vortex patterns are comparable with the vortices states in low kappa type-II superconductors and recently discovered "type-1.5'' superconductors. We also analyze the nearest neighbor distribution of the obtained patterns. (C) 2012 Published by Elsevier B.V.

Abstract: The electrical transport properties of a MoGe thin film with a honeycomb array of nanoscale holes are investigated. The critical current of the system shows nonmatching anomalies as a function of applied magnetic field, enabling us to distinguish between multiquanta vortices trapped in the holes and interstitial vortices located between the holes. The number of vortices trapped in each hole is found to be larger than the saturation number predicted for an isolated hole and shows a nonlinear field dependence, leading to the caging effect as predicted from the Ginzburg-Landau (GL) theory. Our experimental results are supplemented by numerical simulations based on the GL theory.

Abstract: Using a combination of the phenomenological GinzburgLandau theory and micromagnetic simulations, we study properties of a superconducting film with an array of soft magnetic dots on top. An external in-plane magnetic field gradually drives the magnets from an out-of-plane or magnetic vortex state to an in-plane single-domain state, which changes spatially the distribution of the superconducting condensate. If induced by the magnets, the vortexantivortex molecules exhibit rich transitions as a function of the applied in-plane field. At the same time, we show how the magnetic dots act as very effective dynamic pinning centers for vortices in an applied perpendicular magnetic field.

Abstract: We study a mesoscopic superconducting rod with a magnetic dot on its top having its moment oriented along the axis of symmetry. We study the dependence of the vortex pattern with the height and find that for very short and very long rods, the vortex pattern acquires a simple structure, consisting of giant and of multivortex states, respectively. In the long limit, the most stable configuration consists of two vortices, that reach the lateral surface of the rod diametrically opposed. The long rod shows reentrant behavior within some range of its radius and of the dots magnetic moment. Our results are obtained within the Ginzburg-Landau approach in the limit of no magnetic shielding.

Abstract: The magnetic properties of a superconducting disk change dramatically when its dimensions become mesoscopic. Unlike large disks, where the screening currents induced by an applied magnetic field are strong enough to force vortices to accumulate in a 'puddle' at the centre, in a mesoscopic disk the interaction between one of these vortices and the edge currents can be comparable to the intervortex repulsion, resulting in a destruction of the ordered triangular vortex lattice structure at the centre. Vortices instead form clusters which adopt polygonal and shell-like structures which exhibit magic number states similar to those of charged particles in a confining potential, and electrons in artificial atoms. We have fabricated mesoscopic high temperature superconducting Bi2Sr2CaCu2O8+δ disks and investigated their magnetic properties using magneto-optical imaging (MOI) and high resolution scanning Hall probe microscopy (SHPM). The temperature dependence of the vortex penetration field measured using MOI is in excellent agreement with models of the thermal excitation of pancake vortices over edge barriers. The growth of the central vortex puddle has been directly imaged using SHPM and magic vortex numbers showing higher stability have been correlated with abrupt jumps in the measured local magnetisation curves.

Abstract: Within the Ginzburg-Landau theory, we study the vortex structures in three-dimensional anisotropic mesoscopic superconductors in the presence of a uniform magnetic field. Anisotropy is included through varied Tc in different layers of the sample and leads to distinct differences in the vortex states and their free energy. Several unconventional states are found, some comprising vortex clusters or exhibiting asymmetry. In a tilted magnetic field, we found second-order transitions between different vortex states, although vortex entry is generally a first-order transition in mesoscopic samples. In multilayered samples the kinked vortex strings are formed owing to the competing interactions of vortices with Meissner currents and the weak-link boundaries. The length and deformation of vortex fragments are determined solely by the inclination and strength of applied magnetic field, and this lock-in does not depend on the degree of anisotropy between the superconducting layers.

Abstract: We analyze theoretically and experimentally vortex configurations in mesoscopic superconducting squares. Our theoretical approach is based on the analytical solution of the London equation using Green's-function method. The potential-energy landscape found for each vortex configuration is then used in Langevin-type molecular-dynamics simulations to obtain stable vortex configurations. Metastable states and transitions between them and the ground state are analyzed. We present our results of the first direct visualization of vortex patterns in micrometer-sized Nb squares, using the Bitter decoration technique. We show that the filling rules for vortices in squares with increasing applied magnetic field can be formulated, although in a different manner than in disks, in terms of formation of vortex “shells”.