Abstract:
We calculate the density of states of an inhomogeneous superconductor in a magnetic field where the positions of vortices are distributed completely at random. We consider both the cases of s-wave and d-wave pairing. For both pairing symmetries either the presence of disorder or increasing the density of vortices enhances the low energy density of states. In the s-wave case the gap is filled and the density of states is a power law at low energies. In the d-wave case the density of states is finite at zero energy and it rises linearly at very low energies in the Dirac isotropic case (\alpha_D=t/\Delta_0=1, where t is the hopping integral and \Delta_0 is the amplitude of the order parameter). For slightly higher energies the density of states crosses over to a quadratic behavior. As the Dirac anisotropy increases (as \Delta_0 decreases with respect to the hopping term) the linear region decreases in width. Neglecting this small region the density of states interpolates between quadratic and back to linear as \alpha_D increases. The low energy states are strongly peaked near the vortex cores.

Abstract:
The interaction between a superconducting vortex in a type II superconducting film (SC) and a ferromagnet (FM) with out-of-plane magnetization is investigated theoretically within the London approximation. The dependence of the interaction energy on the FM-vortex distance, film thickness and different geometries of the magnetic structures: disk, annulus(ring), square and triangle are calculated. Analytic expressions and vectorplots of the current induced in the SC due to the presence of the FM are presented. For a FM disk with a cavity, we show that different local minima for the vortex position are possible, enabling the system to be suitable to act as a qubit. For FMs with sharp edges, like e.g. for squares and triangles, the vortex prefers to enter its equilibrium position along the corners of the magnet.

Abstract:
In the present work we study an anisotropic layered superconducting film of finite thickness. The film surfaces are considered parallel to the $bc$ face of the crystal. The vortex lines are oriented perpendicular to the film surfaces and parallel to the superconducting planes. We calculate the local field and the London free energy for this geometry. Our calculation is a generalization of previous works where the sample is taken as a semi-infinite superconductor. As an application of this theory we investigate the flux spreading at the superconducting surface.

Abstract:
How out-of-plane disorder affects the electronic structure has been investigated for the single-layer cuprates Bi$_2$Sr$_{1.6}$$Ln$$_{0.4}$CuO$_{6+\delta}$ ($Ln$ = La, Nd, Gd) by angle-resolved photoemission spectroscopy. We have observed that, with increasing disorder, while the Fermi surface shape and band dispersions are not affected, the quasi-particle width increases, the anti-nodal gap is enhanced and the superconducting gap in the nodal region is depressed. The results indicate that the superconductivity is significantly depressed by out-of-plane disorder through the enhancement of the anti-nodal gap and the depression of the superconducting gap in the nodal region.

Abstract:
In quasi low dimensional superconductors under {\it parallel} magnetic fields applied along a conducting direction, vortex lattices with a modulation of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type {\it perpendicular} to the field may occur due to an enhanced paramagnetic depairing. As the strength of an in-plane field is varied in a Q2D material, the Josephson vortex lattices accompanied by nodal planes are formed in higher Landau level (LL) modes of the superconducting (SC) order parameter and show field-induced structural transitions. A change of orientation of nodal planes induced by these transitions should be observed in transport measurements for an out-of-plane current in real superconductors with point disorder effective on the SC layers. Further, the $H_{c2}$-transition from this higher LL state to the normal phase is of second order for moderately strong paramagnetic effects but, in the case with a strong enough paramagnetic effect, becomes discontinuous as well as the transition between this modulated state and an ordinary Abrikosov vortex lattice in the lowest LL. Relevance of these results to recent observations in organic superconductors suggesting the presence of an FFLO state are discussed.

Abstract:
Measurements of magneto-resistivity and magnetic susceptibility were performed on single crystals of superconducting Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$ close to the conditions of optimal doping. The high quality of the investigated samples allows us to reveal a dynamic scaling behaviour associated with a vortex-glass phase transition in the limit of weak degree of quenched disorder. Accordingly, the dissipative component of the ac susceptibility is well reproduced within the framework of Havriliak-Negami relaxation, assuming a critical power-law divergence for the characteristic correlation time $\tau$ of the vortex dynamics. Remarkably, the random disorder introduced by the Fe$_{1-x}$Co$_{x}$ chemical substitution is found to act on the vortices as a much weaker quenched disorder than previously reported for cuprate superconductors such as, e.g., Y$_{1-x}$Pr$_{x}$Ba$_{2}$Cu$_{3}$O$_{7-\delta}$.

Abstract:
We report a study of the basal-plane anisotropy of the superfluid density in underdoped YBa$_{2}$Cu$_{4}$O$_{8}$ (Y124), showing the effects of both the CuO$_{2}$ planes and the fully occupied CuO chains. From small-angle neutron scattering measurements of the vortex lattice, we can infer the superconducting (SC) properties for a temperature ($T$) range $T=$ 1.5 K to $T_{\rm c}$ and magnetic induction $B$ from 0.1 to 6 T. We find that the superfluid density along \textbf{a} has a simple $d$-wave T-dependence. However, along \textbf{b} (the chain direction) the superfluid density falls much more rapidly with $T$ and also with increasing field. This strongly suggests the suppression of proximity-effect induced superconductivity in the CuO chains. In addition, our results do not support a common framework for the low field in-plane SC response in Y124 and related YBa$_{2}$Cu$_{3}$O$_{7}$, and also indicate that any magnetic field-induced charge-density-wave order in Y124 exists only for fields above 6 T.

Abstract:
In a sandwich consisting of two superconducting films, one weakly pinning and one strongly pinning, the vortex positions in both films are determined by the strongly pinning material and the vortex lattice is disordered in both films. We used (strongly pinning) NbN and (weakly pinning) MoGe and studied, by directly imaging the vortex core positions with a scanning tunnelling microscope, how this disorder is restored with increasing thickness of MoGe layer or when the interface is made insulating. For clean interfaces we find that the first reordering of the vortex lattice is found at a layer thickness wich is compatible with the first bending mode of the vortex lines. Making the interface insulating we find that order is restored quickly. We argue that this is can be understood from the competition between the Josephson force working on the vortex segments on the one hand, and the elastic restoring forces inside the weakly pinning layer on the other hand.

Abstract:
The flux line lattice melting transition in two-dimensional pure and disordered superconductors is studied by a Monte Carlo simulation using the lowest Landau level approximation and quasi-periodic boundary condition on a plane. The position of the melting line was determined from the diffraction pattern of the superconducting order parameter. In the clean case we confirmed the results from earlier studies which show the existence of a quasi-long range ordered vortex lattice at low temperatures. Adding frozen disorder to the system the melting transition line is shifted to slightly lower fields. The correlations of the order parameter for translational long range order of the vortex positions seem to decay slightly faster than a power law (in agreement with the theory of Carpentier and Le Doussal) although a simple power law decay cannot be excluded. The corresponding positional glass correlation function decays as a power law establishing the existence of a quasi-long range ordered positional glass formed by the vortices. The correlation function characterizing a phase coherent vortex glass decays however exponentially ruling out the possible existence of a phase coherent vortex glass phase.

Abstract:
In 1993 Tang proposed [1] that vortex avalanches should produce a self organized critical state in superconductors, but conclusive evidence for this has heretofore been lacking. In the present paper, we report extensive micro-Hall probe data from the vortex dynamics in superconducting niobium, where a broad distribution of avalanche sizes scaling as a power-law for more than two decades is found. The measurements are combined with magneto-optical imaging, and show that over a widely varying magnetic landscape the scaling behaviour does not change, hence establishing that the dynamics of superconducting vortices is a SOC phenomenon.