Equilibrium Vortex Research Articles

Multiquantum vortices in conventional superconductors with columnar defects near the upper critical field

Equilibrium vortex configuration in conventional type II superconductors containing columnar defects is theoretically investigated. Near the upper critical field a single defect causes a strong local deformation of the vortex lattice. This deformation has $C_3$ or $C_6$ point symmetry, whose character strongly depends on the vortex-defect interaction. If the interaction is attractive, the vortices can collapse onto defect, while in the case of repulsion the regions free of vortices appear near a defect. Increasing the applied magnetic field results in an abrupt change of the configuration of vortices giving rise to reentering transitions between configurations with $C_3$ or $C_6$ symmetry. In the case of a small concentration of defects these transitions manifest themselves as jumps of magnetization and discontinuties of the magnetic susceptibility.

Comparison of the pinning and the bulk currents in the critical state of a type-II superconductor

The bulk current density distribution in the critical state of a type-II superconductor is studied for different pinning strengths and external magnetic fields. The calculations were made within the extended critical state model for a three-axis ellipsoid, taking into account the equilibrium vortex lattice magnetization caused by the vortex interaction. It is shown that the average current density, J av, could be considerably different from the critical pinning current density, J c, for the magnetic fields not much larger than the lower critical field H c1. The difference between J av and J c result in additional curvature of the local magnetic field profiles and modifies the total moment of the sample which might be important for the analysis of various magnetization experiments.

Equilibrium vortex configurations in domains with boundary

Given a stable configuration of point vortices for steady two-dimensional inviscid, incompressible fluid flow in a domain D D , it is shown that there is another stable configuration of stationary vortices in D D with vortices near the original vortices plus additional vortices near any points on the boundary where the speed of the original flow is a nonzero relative minimum.

Finite-element method to the d-wave time-dependent Ginzburg-Landau equations

We develop an efficient finite-element method to solve the d-wave time-dependent Ginzburg-Landau equations. It is applied to study the equilibrium vortex structure in bulk low and higher κ superconductors as well as in finite-size samples. When the temperature is well below the critical temperature Tc, we reproduce the earlier result that an oblique lattice is more stable than the conventional triangular lattice; while near Tc the triangular lattice is most stable. Also, the effects of a twin boundary on the vortices are examined. This extended finite-element method proves to be flexible to deal with various types of boundary conditions.

Vortex state and dynamics of a d-wave superconductor: Finite-element analysis

The finite-element method is extended to simulate thed-wave time-dependent Ginzburg-Landau equations. By utilizing this method and in the context of the ( s1d)-wave pairing, we discuss the nature of a single vortex, the structure of equilibrium vortex lattices in bulk samples, the nature of vortices in finite-size samples, and most importantly the transport of the vortices. In particular, the low-field free-flux-flow resistivity turns out to obey the law of corresponding states discovered in conventional superconductors, while the high-field resistivity reveals a noticeable effect of the s-wave coupling on lifting the effective upper critical field. The flux flow near and above the depinning current in the presence of a twin boundary or random impurities also assumes a conventional behavior: The current dependence of the flux-flow resistivity can be well described by an overdamped model for a particle subject to driving and pinning forces. However, our results show a noticeable difference between the flux-flow resistivities at large currents in the presence and absence of pinning. @S0163-1829~97!07617-0#

Hydrodynamics of Two-Phase Flow in Gas-Liquid Cylindrical Cyclone Separators

AbstractThis paper presents new experimental data and an improved mechanistic model for the Gas-Liquid Cylindrical Cyclone (GLCC) separator. The data were acquired utilizing a 3" ID laboratory-scale GLCC, and are presented along with a limited number of field data. The data include measurements of several parameters of the flow behavior and the operational envelope of the GLCC. The operational envelope defines the conditions for which there will be no liquid carry-over or gas carry-under. The developed model enables the prediction of the hydrodynamic flow behavior in the GLCC, including the operational envelope, equilibrium liquid level, vortex shape, velocity and holdup distributions and pressure drop across the GLCC. The predictions of the model are compared with the experimental data. These provide the state-of-the-art for the design of GLCC's for the industry.

Simulating the time-dependent dx2-y2 Ginzburg-Landau equations using the finite-element method.

The time-dependent Ginzburg-Landau equations describing a $d$-wave superconductor are simulated by the finite-element method. The equilibrium vortex structure in bulk samples, the nature of vortices in bulk and finite-size samples subject to various types of pinnings, and the transport behaviors are addressed. The extended finite-element method proves to be flexible to deal with various types of boundary conditions, desirable to simulate relaxation processes with very long time scales as well as the dynamics of vortices, especially in high-$\ensuremath{\kappa}$ superconductors.

Dynamic scaling of magnetic flux noise near the Kosterlitz-Thouless-Berezinskii transition in overdamped Josephson junction arrays.

We have used a dc Superconducting QUantum Interference Device to measure the magnetic flux noise generated by the equilibrium vortex density fluctuations associated with the Kosterlitz-Thouless-Berezinskii (KTB) transition in an overdamped Josephson junction array. At temperatures slightly above the KTB transition temperature, the noise is white for $f<f_\xi$ and scales as $1/f$ for $f>f_\xi$. Here $f_\xi\propto\xi^{-z}$, where $\xi$ is the correlation length and $z$ is the dynamic exponent. Moreover, when all frequencies are scaled by $f_\xi$, data for different temperatures and frequencies collapse on to a single curve. In addition, we have extracted the dynamic exponent $z$ and found $z=1.98\pm0.03$.

Optical interferometry in superfluid3He-B

We report interferometric measurements on 0.1 ... 1 mm thick films of superfluid 3He-B. The menisci of three different rotational states of the superfluid were observed and analyzed theoretically using two-fluid hydrodynamics: These are (i) the equilibrium vortex state in which the superfluid and the normal components corotate (solid body rotation), (ii) the vortex-free state (the Landau state), in which only the normal component rotates, and (iii) the quasistationary vortex state in which only the superfluid fraction rotates (pure superfluid rotation). The Landau state manifested itself by a reduced parabolic meniscus at rotation speeds below the critical angular velocity Ω ≲ 0.2 rad/s for vortex formation. Transition from the Landau state to the equilibrium vortex state yielded a sudden deepening of the meniscus when Ωc was exceeded. After a rapid halt of the cryostat, we observed a novel meniscus which was produced by the superfluid rotation while the normal component was at rest. The enhanced depth of this meniscus is governed by the reactive mutual friction parameter B'.By employing laser light, both for imaging and for thermomechanical excitation, we measured the response of a thin superfluid layer to a heat pulse and analyzed it within the theory of two-fluid hydrodynamics. The data were employed, using the dispersion relation for thin film oscillations, to deduce the second viscosity coefficient ζ 3 close to Tc.

Vortex loops entry into type-II superconductors

The magnetic field distribution, the magnetic flux, and the free energy of an Abrikosov vortex loop near a flat surface of type-II superconductors are calculated in the London approximation. The shape of such a vortex line is a semicircle of arbitrary radius. The interaction of the vortex half-ring and an external homogeneous magnetic field applied along the surface is studied. The magnitude of the energy barrier against the vortex expansion into superconductor is found. The possibilities of forming an equilibrium vortex line, determined by the structure of the applied magnetic field, by creating the expanding vortex loops near the surface of type-II superconductors, are discussed.

Vortex equilibrium in film flow near a defect

A simple model based on numerical simulations in bulk is used to examine the pinning characteristics of vortices in helium films adsorbed in the vicinity of substrate defects. The film profile in the absence of a vortex is first calculated including both the Van der Waals potential of a bump defect and surface tension. The displacement and ultimate de-pinning of a vortex line constrained within the profile is then followed as a function of an imposed superfluid flow. The behavior of the vortices lends insight into recent experimental results sensitive to the presence of pinned vortices and indicates that the relevant pinning sites are atomic in dimension.

Vortex statistics in optical speckle fields

An “ensemble of point vortices” approach is introduced to analyze the statistical properties of the chaotic “vortex gas” of optical speckle fields. A peculiar property of the vortex statistics in speckle fields is that the average fraction of pairs of vortices of the same charge among the nearest neighbors is significantly less than 50%. Our approach, which considers optical speckle fields as ensembles of point vortices in thermal equilibrium, interprets this result. The statistical equilibrium distribution of nearest neighbor separation in the point vortex enserble is derived, and the temperature of the speckle field is calculated. The analysis is supported by numerical simulations of the point vortex “billiard”.

Spatial distributions of vortices in sintered YBa 2Cu 3O 7 studied by neutron depolarization

The spatial distributions of vortices in equilibrium (the critical state) in a sintered YBa 2Cu 3O 7 sample are studied by three-dimensional neutron depolarization (3DND), in field and for remanent states. Neutron depolarization provides the magnetization, the length of vortex straightness and the direction cosine of vortex bundles in the sample. By scanning a neutron beam through the sample, the position dependence of these vortex-distribution parameters are determined. From the length of vortex straightness and the position dependence of the magnetization it is found that vortices penetrate between the clusters of grains in small applied field and are pinned in the grain clusters in remanence after a field pulse.

Topological defects in the Abrikosov lattice of vortices in type-II superconductors.

The free energy costs for various defects within an Abrikosov lattice of vortices are calculated using the lowest Landau level approximation (LLL). Defect solutions with boundary conditions for lines to meet at a point (crossing defect) and for lines to twist around each other (braid defect) are sought for 2, 3, 6, and 12 lines. Many results have been unexpected, including the nonexistence of a stable two- or three-line braid. This, and the high energy cost found for a six-line braid lead us to propose that the equilibrium vortex state is not entangled below the irreversibility line of the high-$T_c$ superconductors or in a large part of the vortex-liquid phase above this line. Also, the solution for an infinite straight screw dislocation is found, and used to give a limiting form for the free energy cost of very large braids. This depends on the area enclosed by the braid as well as its perimeter length.

Vortex lattice of layered superconductors in parallel magnetic fields.

In the framework of the Lawrence-Doniach theory, we study numerically the vortex lattice of layered superconductors in parallel magnetic fields for the case of material parameters appropriate to ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{x}}$. In the direction perpendicular to the layers, the period of the vortex lattice is commensurate with that of the layered structure. The lattice structure with each period is obtained numerically from the free- energy functional with the relaxation method, and the lattice constants for the equilibrium state and the dependence of the magnetization on the magnetic field H are determined. For (${\mathit{H}}_{0}$/H${)}^{1/2}$\ensuremath{\gtrsim}4, the magnetization shows a periodic variation in the plot of (${\mathit{H}}_{0}$/H${)}^{1/2}$. (${\mathit{H}}_{0}$ is defined in text.) For higher magnetic fields (${\mathit{H}}_{0}$/H${)}^{1/2}$4, the shape of a unit cell for the equilibrium vortex lattice is enlarged in the direction parallel to the layers, and the magnetization curve deviates from the periodic behavior.

Vortex lattices in layered superconductors.

We study vortex lattices in a superconductor--normal-metal superlattice in a parallel magnetic field. Distorted lattices, resulting from the shear deformations along the layers, are found to be unstable. Under field variation, nonequilibrium configurations undergo an infinite sequence of continuous transitions, typical for soft lattices. The equilibrium vortex arrangement is always a lattice of isocell triangles, without shear.

Rearrangements in steady multiple vortex flows

We are concerned here with steady, inviscid flows in two dimensions which have concentrated regions of vorticity. In particular, we study such flows which {open_quotes}desingularize{close_quotes} a configuration of point vortices in stable equilibrium with an irrotational flow. The vorticity functions in these flows are obtained as solutions of a variational problem for energy set in classes of rearrangements of fixed functions. It is inherent in the formulation of this problem that constraining sets which isolate different t regions of vorticity must be introduced. The existence of solutions of the variational problem follows from results of Burton, but in order for this to provide a flow with a continuous pressure, additional properties must be established. The simplest way to accomplish this is to show that the support of the vorticity is bounded away from the boundary of the constraining set. The major step in our analysis is a {open_quotes}local support lemma{close_quotes} which shows that this is possible under certain circumstances. This generalizes our earlier work for one vortex which in turn builds on results of Turkington. As we show below, it follows from the theory of Burton that for each vortex region {Omega}{sub i} there is a profile function {phi}{sub i}more » such that the vorticity {omega}{sub i} on that region satisfies {omega}{sub i} = {phi}, {omicron} {psi}, where {psi} is the stream function for the flow. Turkington and Eydeland have given an iterative method for computing vortex flows with multiple vortex regions when the profile functions, rather than rearrangement classes, are prescribed in advance. 14 refs, 4 figs.« less

Phase diagram in superconducting multilayers

We theoretically study the vortex states in superconducting multilayers of Nb/NbTi and Nb/NbZr. We solve the Ginzburg-Landau equations numerically and find two different vortex lattices as equilibrium vortex phases. From the free energy calculations, we determine the phase boundary between the vortex phases and map a phase diagram. The magnetization curve exhibits a jump at the phase boundary.

Critical currents in anisotropic crystalline type-II superconductors

Relying on the Mathieu-Simon theory for vortex equilibrium, we derive expressions for the hysteretic magnetization, critical currents and irreversibility field B ∗ of c-axis oriented crystalline films or platelets in normal field. Predictions are compared with currently available data on YBaCuO at 77K.

Surface barrier in the mixed state of type-II superconductors near equilibrium

We have calculated the energy barrier for penetration of straight vortices through a plane surface into a type-II superconductor which contains an equilibrium vortex lattice. The most favorable penetration channel ends with the creation of a creation of a surface interstitial. The height of the barrier is strongly affected by the lattice deformations caused by the penetrating vortex. The proposed mechanism governs the penetration and exit of vortices through the edges of thin superconducting films. The results are in good agreement with experimental values of the barrier obtained by White et al. (Phys. Rev. Lett. 70 (1993) 670) from the edge resistivity of narrow strips of a-MoGe films.