Pinning in type II superconductors

Large and randomly arranged pinning centers cause a strong deformation of a flux line lattice, so that each pinning center acts on the lattice with a maximum force. The average force for such single-particle pinning can be inferred from a simple summing procedure and has a domelike dependence on magnetic field. Pinning centers of average force, such as clusters of dislocations, strongly deform the flux line lattice only in weak fields and in fields close to the critical field, where there is a peak in the dependence of the critical current on magnetic field. In the range of intermediate fields there is a weak collective pinning. A large concentration of weak centers leads to collective pinning in all fields. In this case, near the critical field a critical current peak should be observed. To explain this peak and to define the boundaries between the regions of collective and single-particle pinning the possible break-off of the flux line lattice from the lines of magnetic force should be taken into consideration, which leads to extra softening of the lattice.     

Vortices in anisotropic type-II superconductors

We present a generalized variational model of an isolated vortex, valid in the anisotropic case when the external magnetic field is along one of the symmetry directions. We discuss the effects of the field anisotropy on the core and magnetic pinning of individual vortices.     

Low-temperature properties of anisotropic superconductors with kondo impurities

We present a self-consistent theory of superconductors in the presence of Kondo impurities, using large-N slave-boson methods to treat the impurity dynamics. The technique is tested on the s-wave case and shown to give good results compared to other methods forT _K >T _c . We calculate low temperature thermodynamic and transport properties for various superconducting states, including isotropic s-wave and representative anisotropic model states with line and point nodes on the Fermi surface.     

Pinning of the vortex system and magnetostriction of superconductors

Hard type-II superconductors usually reveal a large, of the order of 10⁻⁵ or 10⁻⁴, magnetostriction in the external magnetic field of several Tesla. Such a strong magnetostriction can be well understood in the framework of the model of the pinning-induced magnetostriction. Although the assumptions of this model are easy to understand, the solution of the problem for realistic sample shapes is difficult, because the stress induced in the sample volume by the screening currents has non uniform distribution and it may also change the sample shape. The model of pinning-induced magnetostriction is insufficient to explain all magnetostriction results in superconductors. Sometimes, it is necessary to consider also other mechanisms of the magnetostriction. Magnetostriction of superconductors was analyzed theoretically and studied experimentally in a large number of both conventional and high temperature superconductors. In this paper we present a review of the most characteristic results. We also present the phenomenon of giant magnetostriction jumps, which is closely related to the phenomenon of giant flux jumps or thermomagnetic instabilities in type-II superconductors.     

Viscous flux motion in anisotropic magnetic superconductors

Magnetic field penetrates in the form of flux lines or vortex thread into type-II magnetic superconductors (MSC) and induces magnetization of magnetic subsystem over a distance of an order of the London penetration depth surrounding the normal cores. When a flux line moves by, surrounding magnetization moves as a whole through the sample and a free motion of vortices is subjected to magnetic viscous drag, giving rise to dissipation. The flux flow resistance in the mixed state of anisotropic MSC has been studied on the basis of the London theory. Expressions for the dissipation and viscosity coefficient associated with the change of the magnetic subsystem as a vortex moves about are derived.     

Vortex lines and field reversal in anisotropic superconductors

In an anisotropic superconductor, a vortex line which is not parallel to a symmetry axis can have surprising features in its magnetic field pattern. In this paper we examine one such feature, the reversal of the component of the magnetic field parallel to the vortex axis. This field reversal leads to an attractive interaction between two parallel lines, when their positions satisfy certain criteria. Using perturbation theory, we develop simple analytic results which allow us to identify the supercurrents responsible for the magnetic field pattern. The importance of different screening lengths is stressed.     

On the critical temperature of anisotropic superconductors

An approximate analytic formula for the increase in the superconducting critical temperature caused by anisotropy is derived and compared with both the results of exact numerical solutions of the Eliashberg equations and with a previous approximate formula due to Allen and Butler. In all the cases considered our new formula is found to be more accurate than the previous one and to agree reasonably well with the exact results for the intermediate and weak coupling superconductors considered.Research supported by the Natural Sciences and Engineering Research Council of Canada.     

Vortex motion in type II superconductors with controllable type defects

A model that connects the nonlinearity of the voltage-current characteristicsV(I) in the mixed state with the statistical distribution of the pinning forces acting on moving vortices is considered. The role of the elastic properties of the vortex lattice in theV(I) behavior is discussed. A method for obtaining the statistical distribution parameters of the pinning force from experimentalV(I) data is considered, based on experimental data onV(I) dependences in Al-Ag. In alloys with controllable defects, the distribution parameters of the pinning force can be found and connected with typical parameters of the defect structure of the specimen.     

Flux motion in anisotropic type-II superconductors nearH c 2 with arbitrary vortex orientation

Flux motion in anisotropic type-II superconductors near H_{c 2} is studied in the framework of the time-dependent Ginzburg-Landau (TDGL) theory for the case that the average flux densityB is oriented in an arbitrary direction relative to the principal axes of the sample. The linearized TDGL equation for a uniformly translating order parameter is solved and expressions for all elements of the flux-flow resistivity tensor _ij (including the off-diagonal Hall elements) are obtained. The diagonal elements _ii show the angular scaling property that _ii(B) = _ii(B/H_{c 2}(, ø)), whereas the Hall elements _ij (i j) have additional angular dependences that are not contained in H_c2. For the case that the normal state Hall elements _ij ⁽ⁿ⁾ B _k with i j k, the ratios _ij/ _ij ⁽ⁿ⁾ are functions of B/H_c2 (, ) only.     

The upper critical field and dimensional crossover in superconductors with anisotropic electron spectrum

The theory of superconductivity in metallic superstructures with anisotropic electron spectrum is presented. It is shown that these structures, three-dimensional in the normal state, become layered or fibrous in the superconducting state. The upper critical magnetic field changes the temperature dependence in the vicinity of the critical temperature from one (two)-dimensional to three-dimensional.     

Pinning Effects in Nb Thin Films with Artificial Pinning Arrays

We summarize some results on the behavior of vortex dynamics and pinning effects in superconducting films with artificial pinning centers. Superconducting thin films with regular arrays of holes were fabricated using electron-beam lithography and reactive dry etching techniques. Vortex dynamics in the mixed state in type II superconductors is strongly influenced by the presence of defects, which act as pinning centers. Periodic critical current matching peaks were observed in magnetotransport measurements. The matching effect is caused by the interplay between the pinning centers and vortex lattice. Therefore, vortex lattice behaviors are changed for different temperatures and the geometry of the pinning centers. Molecular dynamic simulations are made to study this phenomenon. The ground state distribution of vortices obtained from simulations can give a reasonable explanation of the prominent matching peaks we found in the experiments.     

Roles of oxygen defects in copper oxide superconductors

Oxygen vacancy and interstitial defects can have a profound effect on the superconducting properties of copper oxide compounds. Recent work on compounds such as La₂CuO_4+x and HgBa₂CuO_4+x has provided new insight into the role of interstitial oxygen defects as a doping mechanism. The number of carriers created by each interstitial defect depends on the local defect structure. Studies of (La, Sr, Ca)₃Cu₂O_6+x with various metal compositions and metalsite ordering show that interstitial oxygen defects that form between the CuO₂ layers in this structure systematically lowerT _c and eventually destroy superconductivity. Conversely, oxygen vacancies in the CuO₂ planes have surprisingly little effect at concentrations below 3%. The infinite-layer compounds, ACuO₂, where A=La, Sr, Ca, Nd, etc., in solid-solution combinations, could offer a similar environment for the formation of interstitial oxygen defects between the CuO₂ planes, allowing interstitial oxygen defects to contribute to the doping of these compounds. However, neutron diffraction experiments on Sr_0.9La_0.1CuO₂ (T _c = 42 K) have not found any interstitial oxygen.     

Effect of normal impurities on anisotropic superconductors with variable density of states

We develop a generalized BCS theory of impure superconductors with an anisotropic electron-electron interaction represented by the factorizable model introduced by Markowitz and Kadanoff, and a variable electronic density of statesN(), assumed to peak at the Fermi energy, which is modeled by a Lorentzian superimposed on a uniform background. As the impurity scattering is increased, the enhancement ofT _c by both the anisotropy and the peak inN() is washed out. The reduction is investigated for different values of the anisotropy and different peak heights and widths. It is concluded that the effects of anisotropy and the peak are reduced together in such a way that any effect due to anisotropy is not easily distinguishable from that due to the peak.Research supported by the Natural Sciences and Engineering Research Council of Canada and the McMaster University Science and Engineering Research Board.     

On the BCS theory of paramagnetic impurities in anisotropic superconductors

We develop a theory based on BCS theory which treats the effect of paramagnetic impurities in an anisotropic superconductor. It is found that in a separable model for the order parameter its anisotropy is expected to increase with increasing concentration of paramagnetic impurities. The critical temperature, the order parameter, and the quasiparticle density of states are computed numerically from our theoretical results. We find that there exists a regime which is superconducting by virtue of the fact that the paramagnetic impurities make the material highly anisotropic. In this regime the critical temperature can be reduced rapidly to zero by adding dilute concentrations of normal scattering impurities.Research supported by the Natural Sciences and Engineering Research Council of Canada.This paper is dedicated on the occasion of the 70th birthday of Prof. Dr. E. Ledinegg, head of the Institut für Theoretische Physik, Technische Universität, Graz, Austria.     

Transition temperature of anisotropic superconductors with Kondo impurities: Square well model

The Eliashberg equations for an anisotropic superconductor containing Kondo impurities are approximated analytically using the square well model for the electron-phonon interaction. Anisotropy is incorporated via a separable model and the impurities are treated within the Matsuura, Ichinose, and Nagaoka (MIN) formalism. Explicit expressions for the reduction of the superconducting transition temperature are obtained. The derived formulas are generalizations of the MIN results to include both anisotropy and weak electron-phonon coupling effects.     

Two-dimensional line defects in anisotropic elastic solids

The Stroh formalism and analytic continuation approach are used to develop a systematic study for two-dimensional line defects in anisotropic elastic solids. The line defects are classified as either belonging to the craze type or line inhomogeneity type. A crack and rigid line are considered as two special cases of these categories. The governing equations, given in terms of the Stroh matrix notation, show many complementary features between these two line defects. In addition, a discussion is given showing why the line defect field cannot in general be developed from the Eshelby inclusion solution [1], except for the special cases of a crack and rigid line inhomogeneity.     

Critical currents of NbTi tapes with differently oriented anisotropic defects

In the paper we present a theory predicting the angular dependence of the critical current in NbTi tapes with elongated defects of different orientation with respect to the tape axis. Corresponding experiments were carried out on samples made from two NbTi foils with different critical current densities.The role of the self-field as well as of the small additional perpendicular field on the critical current is also investigated.