Vortex Escape from Columnar Defect in a Current-Loaded Superconductor

The problem of Abrikosov vortices depinning from extended linear (columnar) defect in 3D-anisotropic superconductor film under non-uniformly distributed Lorentz force is studied for the case of low temperatures, disregarding thermal activation processes. We treat it as a problem of mechanical behavior of an elastic vortex string settled in a potential well of a linear defect and exerted to Lorentz force action within the screening layer about the London penetration depth near the specimen surface. The stability problem for the vortex pinning state is investigated by means of numerical modeling, and conditions for the instability threshold are obtained as well as the critical current density \(j_\mathrm{c}\) and its dependence on the film thickness and magnetic field orientation. The instability leading to vortex depinning from extended linear defect first emerges near the surface and then propagates inside the superconductor. This scenario of vortex depinning mechanism at low temperatures is strongly supported by some recent experiments on high-Tc superconductors and other novel superconducting materials, containing columnar defects of various nature.     

Cutting of bent vortex lines

One of the major problems in the application of type II superconductors is the appearance of resistivity in cases where a current-carrying specimen is in a longitudinal magnetic field. This is explained by the onset of flux-line cutting events, followed by cross-joining of the line parts. The calculation given here shows the amount of repulsive force and energy between two curved vortex lines and examines the general stability of the vortex-vortex system. First, the actual interaction potential between curved vortices is computed. It includes all electromagnetic and core overlap terms of interaction and self-interaction, and allows computation of the system energy under all curved vortex-line configurations. A computer program is used to find the form of lowest free energy. To do this, special trial functions are established to describe the three-dimensional form of the vortex-vortex system. In these functions parameters determine the qualitative and quantitative form. The asymptotic boundary conditions are built into the nature of the trial functions. The computer program now minimizes the free energy with respect to these parameters. The resulting repulsive energy and force are more than ten times less than the known results for straight flux lines, especially for small asymptotic cutting angles. There is no sharp maximum in the plot of repulsive force versus flux-line separation. A remarkable result is the loss of general stability below a separation distance of several London penetration depths, depending on the cutting angle and the Ginzburg-Landau parameter. The explanation lies in the local attraction of central sections of the vortices as a result of configurational adaptation. This explains the onset of resistance at small currents and small magnetic fields.     

Liquid 4He: Contributions to First Principles Theory. I. Quantized Vortices and Thermohydrodynamic Properties

Quantized vortices in liquid ⁴ He are treated quantum mechanically with realistic many-body model wave functions in variational calculations for energy and core structure at T = 0 K. A rectilinear vortex and both small and large vortex rings are studied. Calculated results indicate that rotons are not just small-quantized vortex rings. We compare our results for quantized vortices with experimental data and with theoretical results calculated by others. Correlated basis functions and standard statistical mechanics are used in treating thermohydrodynamic properties of flowing liquid ⁴ He. The Helmholtz potential is evaluated for a model of the flowing liquid that includes phonons and interacting rotons. Characteristics of this potential are discussed. The physical nature of negative superfluid density is explained. Superfluid density, entropy, and specific heat for liquid He-II are evaluated using our theory and the results are compared with experimental data. Very good agreement is found, except in a small temperature range near the λ transition. We indicate that results obtained here can be used in extending the theory to include thermally excited vortices and to investigate the possible role of vortices in accounting for the λ transition in liquid ⁴ He.      

Vortex formation and dissolution in sheared sands

Using digital image correlation, we track the displacement fluctuations within a persistent shear band in a dense sand specimen bounded by glass walls undergoing plane strain compression. The data evidences a clear, systematic, temporally recurring pattern of vortex formation, dissolution, and reformation throughout macroscopic softening and critical state regimes. During softening, locally affine deformation zones are observed at various locations along the shear band, which we argue to be kinematic signatures of semi-stable force chains. Force chain collapse then occurs, inducing vortex formation. Local jamming at the conflux of opposing displacements between adjacent vortices arrests the vortices, providing an avenue for potential new force chains to form amidst these jammed regions. The process repeats itself temporally throughout the critical state. The pattern further correlates with fluctuations in macroscopic shear stress. We characterize the nature of the observed vortices, as they are different in our sands comprised of irregular shaped particles, as compared to previous observations from experiments and numerical simulations which involved circular or rounded particles. The results provide an interesting benchmark for behavior of non-circular/non-spherical particles undergoing shear.     

A vortex method for separated flow around an airfoil with a detached spoiler

A discrete vortex method based on no-slip condition is developed for simulating unsteady separated flows around an airfoil with a detached spoiler. For flow separated at each sharp edge, such as the spoiler tips and the trailing edge of the airfoil, a vortex sheet is used to feed discrete vortices at each time step. The length, inclination and strength of each sheet is determined by the continuity equation, the momentum principle and a Kutta pressure condition such that the flow, net force and pressure difference across the vortex sheet are all zero. The separation on the airfoil upper surface is simulated by discrete vortices shed from a fixed separation point. The flow patterns behind a detached spoiler at different time steps are obtained and compared with those of the conventional spoiler. Reasonable agreements are found between the predicted pressure distributions and experimental measurements. The computed results show that base-venting changes the flow field around the spoiler and reduces the adverse effect in lift experienced by the airfoil when the spoiler undergoes a rapid deployment.     

Accelerating the annihilation of an optical vortex dipole in a Gaussian beam

When a Gaussian beam with two oppositely charged vortices propagates in free space, these two vortices will move around on the transverse beam plane. They may either move toward each other and annihilate each other spontaneously or survive all the way depending on the conditions. Here, we investigate how to force vortex dipoles to annihilate. We find that the background phase function created by two oppositely charged vortices during beam propagation can cause the vortices to move together and annihilate each other. The background phase function on a transverse plane just beyond the point where a dipole annihilated is continuous and retains the potential that forces a dipole to annihilate. We use this background phase function to accelerate the annihilation of vortex dipoles. Numerical results are provided to show the acceleration of dipole annihilation in a Gaussian beam, using such a background phase function.     

Dynamical Properties of Vortices in a Bose-Einstein Condensate in a Rotating Lattice

We present simulation results of the vortex dynamics in a trapped Bose-Einstein condensate in the presence of a rotating optical lattice. Changing the potential amplitude and the relative rotation frequency between the condensate and the optical lattice, we find a rich variety of dynamical phases of vortices. In particular, when the optical lattice rotates faster than the condensate, the competition between the pinning force and the interactions by nucleated interstitial vortices leads to the melting of vortex lattice, yielding a vortex liquid phase.     

Nucleation of Bubbles on quantized vortices in helium-4

We consider the properties of vortices in superfluid helium-4 at negative pressure. Based on a simple density-functional model, we first calculate the density profile in the vicinity of a vortex. We then determine the negative pressure at which the vortex becomes unstable against a uniform radial expansion all along its length. This instability occurs at –6.9 bars. We then calculate the pressure-dependence of the energy E_nuc required to nucleate a bubble on the vortex. The results of this calculation are used to estimate the effect of quantized vortices on the rate at which bubbles are nucleated in superfluid helium at negative pressure.     

Vortex Molecules in Thin Films of Layered Superconductors

Both the equilibrium and transport properties of the vortex matter are essentially affected by the behavior of the intervortex interaction potential. In isotropic bulk superconductors this potential is well known to be repulsive and is screened at intervortex distances R greater than the London penetration depth λ. As a result, in perfect crystals quantized Abrikosov vortices form a triangular lattice. In thin films of anisotropic superconductors this standard interaction potential behavior appears to be strongly modified because of the interplay between the long-ranged repulsion predicted in the pioneering work by J. Pearl and the attraction caused by the tilt of the vortex lines with respect to the anisotropy axes. This interplay results in a new type of vortex arrangement formed by finite-size vortex chains, i.e., vortex molecules. Tilted vortices with such unusual interaction potential form clusters with the size depending on the field tilting angle and film thickness or/and can arrange into multiquanta flux lattice. The magnetic flux through the unit cells of the corresponding flux line lattices equals to an integer number N of flux quanta. Thus, the increase in the field tilting (or varying temperature) should be accompanied by the series of the phase transitions between the vortex lattices with different N. A similar scenario should be realized in strongly anisotropic BSCCO high-T _c superconductors where in tilted field a crossing lattice of Abrikosov vortices (the stacks of pancakes in this case) and Josephson vortices appears. This crossing leads to the zigzag deformation of the pancakes stacks which is responsible for the attraction interaction competing with the long-ranged Pearl’s repulsion.     

High-power efficient multiple optical vortices in a single beam generated by a kinoform-type spiral phase plate

We propose using a solitary kinoform-type spiral phase plate structure to generate an array of vortices located in a single beam. Kinoform-type spiral surfaces allow each wavelength component of the phase modulation value to be wrapped back to its 2 pi equivalent for optical vortices of high charge. This allows the surface-relief profiles of high-charge vortices to be microfabricated with the same physical height as spiral phase plates of unity-charged optical vortices. The m-charged optical vortex obtained interacts with the inherent coherent background, which changes the propagation dynamics of the optical vortex and splits the initial m charge into /m/ unity-charged optical vortices within the same beam. Compared to a hologram, a multistart spiral phase plate is more efficient in the use of available spatial frequencies and beam energy and also is computationally less demanding. Furthermore, using microfabrication techniques will allow for greater achievable tolerances in terms of smaller feature sizes.     

Role of Interstitial Pinning in the Dynamical Phases of Vortices in Superconducting Films

We analyze the vortex dynamics in superconducting thin films with a periodic array of pinning centers. In particular, we study the effect of anisotropy for a Kagomé pinning network when longitudinal and transverse transport currents are applied. By solving the equations of motion for the vortex array numerically at zero temperature, we find different phases for the vortex dynamics, depending on the pinning and driving force. An unusual sequence of peaks for driving force along and perpendicular to the main lattice axes is observed for the differential resistance, reflecting the anisotropy of the transport properties and the complex behavior of the vortex system. This behavior may be understood in terms of interstitial pinning vacancies, which create channels of vortices with different pinning strengths.     

Vortex Dynamics in Bi2Sr2CaCu2O8 Single Crystal with Low Density Columnar Defects Studied by Magnetic Force Microscope

We have studied vortex dynamics in Bi₂Sr₂CaCu₂O₈ single crystal with low density columnar defects by using a magnetic force microscope. Single crystal Bi₂Sr₂CaCu₂O₈ sample was irradiated by 1.3 GeV uranium ion to form artificial pinning centers along the crystalline c-axis. The irradiation dose corresponded to a matching field of 20 gauss. The radius of an individual vortex is approximately 140 nm, which is close to the penetration depth of this material. Magnetic force microscope (MFM) images show that intrinsic crystalline defects such as stacking fault dislocations are very effective pinning centers for vortices in addition to the pinning centers due to ion bombardment. By counting the number of vortex, we found that the flux trapped at each pinning center is a single flux quantum. At higher magnetic field, the vortex structure showed an Abrikosov lattice disturbed only by immobile vortices located at pinning centers. When increasing or decreasing the external magnetic field, the spatial distribution of vortices showed a Bean model like behavior.     

Optimal annular computer-generated holograms for the generation of optical vortices

We analyze a method for efficiently generating optical vortices by use of annular computer-generated holograms and a spatial light modulator. We found that there exists an optimal annular width by which the reconstructed vortex ring in the focal plane has the steepest gradient and the worthless subbright rings can be largely suppressed. We fitted a general formula for determining the value of this optimal annular width and propose a method for designing a multiring structure of optical vortices and specialized interferometric vortex patterns. Finally, we discuss the situation of a Gaussian beam as illuminated light and find that there exists an optimal beam waist that results in the best energy efficiency.     

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.     

Majorana States in 2D Topological Superconductor Hosting Abrikosov Vortices

We study Majorana states near Abrikosov vortices in a 2D topological superconductor in the applied magnetic field B. The Majorana fermions always arise in pairs. In the considered case, the first Majorana fermion localizes in the vortex core while the second, exterior, Majorana fermion localizes at the distance r ∝ 1/B away from the core. We calculate the hybridization between the vortex-core and the exterior Majorana fermions in the cases of a single vortex, two vortices, and the Abrikosov vortex lattice. We show that the hybridization can be effectively governed by the applied magnetic field if the chemical potential is tuned near the Dirac point. We also show that in the case of the vortex lattice, the hybridization between the vortex-core and external Majorana fermions affects significantly low-energy spectrum giving rise to the gap between two lowest Majorana energy bands.     

Vortex motion in the early stages of unsteady flow around a circular cylinder

In this paper, processes in the early stages of vortex motion and the development of flow structure behind an impulsively-started circular cylinder at high Reynolds number are investigated by combining the discrete vortex model with boundary layer theory, considering the separation of incoming flow boundary layer and rear shear layer in the recirculating flow region. The development of flow structure and vortex motion, particularly the formation and development of secondary vortex and a pair of secondary vortices and their effect on the flow field are calculated. The results clearly show that the flow structure and vortices motion went through a series of complicated processes before the symmetric main vortices change into asymmetric: development of main vortices induces secondary vortices; growth of the secondary vortices causes the main vortex sheets to break off and causes the symmetric main vortices to become “free” vortices, while a pair of secondary vortices is formed; then the vortex sheets, after breaking off, gradually extend downstream and the structure of a pair of secondary vortices becomes relaxed. These features of vortex motion look very much like the observed features in some available flow field visualizations. The action of the secondary vortices causes the main vortex sheets to break off and converts the main vortices into free vortices. This should be the immediate cause leading to the instability of the motion of the symmetric main vortices. The flow field structure such as the separation position of boundary layer and rear shear layer, the unsteady pressure distributions and the drag coefficient are calculated. Comparison with other results or experiments is also made. This work was presented at the First Asian Congress of Fluid Mechanics, Bangalore in December 1980.     

Computer simulation of vortex pinning in type II superconductors. I. Two-dimensional simulation

The summation of pinning forces to a volume force exerted on the vortex lattice in type II superconductors allowing it to carry a loss-free current is not fully understood. In order to clarify this question we have started computer simulations of flux pinning. It is shown that for many experimental situations bending of vortices may be neglected since the vortices are too short or pinning is too weak, and thus pinning is two-dimensional. As a first step, two-dimensional pinning simulations will thus be instructive with regard to, say, ribbons of amorphous metals. A general expression for the energy of a vortex-pin system in two and three dimensions is given. The simulation method is presented and illustrated for the isolated pin (with a detailed discussion of the “threshold effect” and of elastic instabilities) and for pin “walls” (grain boundaries) and “nozzles.” Random point pins acting on a perfect or defective vortex lattice are treated in an accompanying paper.     

Phase transitions in the growth of4He films

Using a microscopic, variational approach we examine the growth of⁴He absorbed to graphite and alkali substrates. We find that superfluid layers are formed and their behavior as a function of coverage is closely related to the one of a purely two-dimensional superfluid. The growth of a new layer undergoes a phase transition from a cluster formation into the connected superfluid when the coverage is increased. Based on the important connection to the two-dimensional fluid we propose a microscopic theory of quantum vortices in⁴He films at zero temperature, in which single vortices are treated as quasiparticles. We calculate the energy needed to create the single vortex, vortex inertial mass, microscopic interaction between vortices and binding energy of the vortex-antivortex pair as a function of density. We predict that at the⁴He superfluid density less than about 0.037 Å^–2 the binding energy of the pair becomes negative, indicating a phase transition into a new state where vortex-antivortex pairs are spontaneously created.     

Dynamics of Quantized Vortices in Superfluid Helium and Rotating Bose-Einstein Condensates

No Heading We study theoretically and numerically the dynamics of quantized vortices in superfluid helium and rotating Bose-Einstein condensates. After reviewing briefly the recent motivation, we discuss these topics with the emphasis on the research done by our group. One of the modern important problems is how superfluid turbulence relates to classical turbulence. First, we show that superfluid turbulence consisting of a vortex tangle has an energy spectrum consistent with the Kolmogorov law. Second, we discuss the vortex states that appear in a rotating channel with counterflow. In the field of atomic-gas Bose-Einstein condensation, the dramatic observations of quantized vortices were made for rotating condensates. By solving numerically the Gross-Pitaevskii equation, we found a whole story of the vortex lattice formation consistent with the observations.PACS numbers: 67.40.Vs, 47.32.Cc, 47.37.+q.