Abstract:
Magnetoresistance and radio frequency penetration depth techniques are used to study grain connectivity and broadening of superconducting transition. We study and compare these issues in clean polycrytalline samples of three different superconducting systems e.g. MgB2, NbSe2 and Bi2Sr2Ca2Cu3O10. From the rf response, the bulk pinning force constant is evaluated. From high field transport measurements, H-T phase diagram is ascertained for the three systems with varying degrees of fluctuation and connectivity.

Abstract:
The resistive transition of granular high-T$_c$ superconductors, characterized by either weak (YBCO-like) or strong (MgB$_2$-like) links, occurs through a series of avalanche-type current density rearrangements. These rearrangements correspond to the creation of resistive layers, crossing the whole specimen approximately orthogonal to the current density direction, due to the simultaneous transition of a large number of weak-links or grains. The present work shows that exact solution of the Kirchhoff equations for strongly and weakly linked networks of nonlinear resistors, with Josephson junction characteristics, yield the subsequent formation of resistive layers within the superconductive matrix as temperature increases. Furthermore, the voltage noise observed at the transition is related to the resistive layer formation process. The noise intensity is estimated from the superposition of voltage drop elementary events related to the subsequent resistive layers. At the end of the transition, the layers mix-up, the step amplitude decreases and the resistance curve smoothes. This results in the suppression of noise, as experimentally found. Remarkably, a scaling law for the noise intensity with the network size is argued. It allows to extend the results to networks with arbitrary size and, thus, to real specimens.

Abstract:
We microscopically examine the intergrain Josephson current in iron-pnictide superconductors in order to solve the puzzle of why the intergrain current is much lower than the intragrain one. The theory predicts that the intergrain Josephson current is significantly reduced by the $\pm$s-wave symmetry when the incoherent tunneling becomes predominant and the density of states and the gap amplitude between two bands are identical. We find in such a situation that the temperature dependence of the intergrain Josephson current shows an anomalously flat curve over a wide temperature range. Finally, we suggest important points for increasing the intergrain current.

Abstract:
The resistivity behavior of inhomogeneous superconductors with random $\pi$ junctions, as in high-$T_c$ materials with d-wave symmetry, is studied by numerical simulation of a three-dimensional XY spin glass model. Above a concentration threshold of antiferromagnetic couplings, a resistive transition is found in the chiral-glass phase at finite temperatures and the critical exponents are determined from dynamic scaling analysis. The power-law exponent for the nonlinear contribution found in recent resistivity measurements is determined by the dynamic critical exponent of this transition.

Abstract:
We introduce a model describing vortices in strongly disordered three-dimensional superconductors. The model focuses on the topological defects, i.e., dislocation lines, in an elastic description of the vortex lattice. The model is studied using Monte Carlo simulations, revealing a glass phase at low temperatures, separated by a continuous phase transition to the high temperature resistive vortex liquid phase. The critical exponents nu ~ 1.3 and eta ~ -0.4 characterizing the transition are obtained from finite size scaling.

Abstract:
A characterization of the magnetic superconductors RuSr2GdCu2O8 [Ru-(1212)] and RuSr2(Gd1.5Ce0.5)Cu2O10 [Ru-(1222)] through resistance measurements as a function of temperature and magnetic field is presented. Two peaks in the derivative of the resistive curves are identified as intra- and intergrain superconducting transitions. Strong intragrain granularity effects are observed, and explained by considering the antiphase boundaries between structural domains of coherently rotated RuO6 octahedra as intragrain Josephson-junctions. A different field dependence of the intragrain transition temperature in these compounds was found. For Ru-(1212) it remains unchanged up to 0.1 T, decreasing for higher fields. In Ru-(1222) it smoothly diminishes with the increase in field even for a value as low as 100 Oe. These results are interpreted as a consequence of a spin-flop transition of the Ru moments. The large separation between the RuO2 layers in Ru-(1222) promotes a weak interlayer coupling, leading the magnetic transition to occur at lower fields. The suppression rate of the intragrain transition temperature is about five times higher for Ru-(1222), a result we relate to an enhancement of the 2D character of the vortex structure. A distinctive difference with conventional cuprates is the sharp increase in amplitude of the intergrain peak in both systems, as the field is raised, which is ascribed to percolation through a fraction of high quality intergrain junctions.

Abstract:
The evolution of thermomagnetic perturbations in the resistive state of superconductors is considered. A qualitative pattern of the formation and further development of nonlinear stationary structures that describe the final stage of thermal and electromagnetic perturbations in a superconductor is investigated. The wave propagation velocity and the wave front width in a superconductor are estimated.

Abstract:
We suggest a novel nonlinear $\sigma$-model for the description of disordered superconductors. The main distinction from existing models lies in the fact that the saddle point equation is solved non-perturbatively in the superconducting pairing field. It allows one to use the model both in the vicinity of the metal-superconductor transition and well below its critical temperature with full account for the self-consistency conditions. We show that the model reproduces a set of known results in different limiting cases, and apply it for a self-consistent description of the proximity effect at the superconductor-metal interface.

Abstract:
We revise the problem of the density of states in disordered superconductors. Randomness of local sample characteristics translates to the quenched spatial inhomogeneity of the spectral gap, smearing the BCS coherence peak. We show that various microscopic models of potential and magnetic disorder can be reduced to a universal phenomenological random order parameter model, whereas the details of the microscopic description are encoded in the correlation function of the order parameter fluctuations. The resulting form of the density of states is generally described by two parameters: the width Gamma measuring the broadening of the BCS peak, and the energy scale Gamma_{tail} which controls the exponential decay of the density of the subgap states. We refine the existing instanton approaches for determination of Gamma_{tail} and show that they appear as limiting cases of a unified theory of optimal fluctuations in a nonlinear system. Application to various types of disorder is discussed.

Abstract:
Layered singlet paired superconductors with disorder and broken time reversal symmetry are studied. The phase diagram demonstrates charge-spin separation in transport. In terms of the average intergrain transmission and the interlayer tunnelling we find quantum Hall phases with spin Hall coefficients of 0 and 2 separated by a spin metal phase. We identify a spin metal-insulator localization exponent as well as a spin conductivity exponent of ~0.9. In presence of a Zeeman term an additional phase with spin Hall coefficient of 1 appears.