Vortex-vortex Interactions Research Articles

Scanning Hall probe microscopy of unconventional vortex patterns in the two-gap MgB2superconductor

The low magnetic field vortex patterns nucleation and evolution in a high-quality two-gap superconductor MgB${}_{2}$ single crystal have been investigated by low-temperature scanning Hall probe microscopy. Large areas have been imaged with single-vortex resolution while changing systematically the thermodynamic parameters for field and temperature. The obtained patterns have been studied and compared with those of a reference 2H-NbSe${}_{2}$ single crystal. We found that the observed vortex patterns in MgB${}_{2}$ (e.g., stripes, clusters) appear due to competing vortex-vortex interactions as suggested by the theory of type-1.5 superconductivity.

Unpinning triggers for superfluid vortex avalanches

The pinning and collective unpinning of superfluid vortices in a decelerating container is a key element of the canonical model of neutron star glitches and laboratory spin-down experiments with helium II. Here the dynamics of vortex (un-)pinning is explored using numerical Gross-Pitaevskii calculations, with a view to understanding the triggers for catastrophic unpinning events (vortex avalanches) that lead to rotational glitches. We explicitly identify three triggers: rotational shear between the bulk condensate and the pinned vortices, a vortex proximity effect driven by the repulsive vortex-vortex interaction, and sound waves emitted by moving and repinning vortices. So long as dissipation is low, sound waves emitted by a repinning vortex are found to be sufficiently strong to unpin a nearby vortex. For both ballistic and forced vortex motion, the maximum inter-vortex separation required to unpin scales inversely with pinning strength.

Effect of columnar grain boundaries on flux pinning in MgB2 films

Columnar grain boundaries are widely known to be a very effective source for flux pinning in MgB2 films. In this study, we have investigated the pinning effect of a columnar grain boundary at various temperatures of 5, 10, 20, 30, and 35 K in columnar structured MgB2 films with an average grain size of ∼300 nm. The average vortex-vortex spacing (a0) is estimated at a specific magnetic field, Bpeak, where the Bpeak is the magnetic field when the flux pinning force density (Fp) reaches a maximum. The values of a0/2, which largely affect the vortex-vortex interaction, are much closer to the coherence length of MgB2, than to the penetration depth, which indicates that the vortices can be strongly pinned to the columnar grain boundaries. Furthermore, we found that the columnar grain boundaries acted as strong pinning sources over a wide temperature region, although their effectiveness began to lessen slowly at temperatures above ∼20 K, which was determined on the basis of the flux-line lattice-shearing mechanism.

Strong vortex pinning in FeSe0.5Te0.5 epitaxial thin film

We report on the magnetic field and angular dependence of the critical current density of epitaxial FeTe0.5Se0.5 thin films. The films exhibit high critical current values and weak dependence on the applied magnetic field. The Jc is larger for field parallel to the c-axis, which is the opposite behavior of what expected from the critical field anisotropy. The analysis of the activation energy for vortex motion indicates that the single pinning regime holds up to 9 T, suggesting that correlated pinning centers are more effective than the vortex-vortex interaction even at the largest applied fields. Scanning tunneling microscope analysis indicates threading dislocations as possible pinning centers.

Study of instabilities and transitions for a family of quasi-two-dimensional magnetohydrodynamic flows based on a parametrical model

In this study, flow phenomena associated with inflectional and boundary-layer instabilities, as well as a mixed instability mode in quasi-two-dimensional magnetohydrodynamic flows in a rectangular duct are accessed with the help of a parametrical model, where the basic velocity profile with near-wall jets and associated points of inflection are produced by imposing an external flow-opposing force. By varying this force, various instability modes and transition scenarios are reproduced. First, linear stability analysis is performed and then nonlinear effects are studied using direct numerical simulation for Hartmann numbers 100 and 200 and Reynolds numbers from 1800 to 5000. A special attention is paid to the location of the inflection point with respect to the duct wall. A more complex flow dynamics, including various vortex-wall and vortex-vortex interactions, and even negative turbulence production are observed and analyzed as the inflection point approaches the wall. The analysis of obtained results and their comparison with relevant data for magnetohydrodynamic duct flows gain an insight into what is typically called “jet instability,” including linear and nonlinear mechanisms.

Guided vortex motion in YBa2Cu3O7thin films with collective ratchet pinning potentials

We investigate guided vortex motion in high-temperature YBa${}_{2}$Cu${}_{3}$O${}_{7}$ thin films patterned with an array of asymmetric blind antidots. A preferential vortex motion along spatial asymmetric pinning potentials has been directly observed by changing the driving current direction. Transport measurements reveal that effective ratchet potentials are created by fixed vortices strongly pinned within the antidots while the spatial asymmetry is transferred to interstitial vortices. We study a novel ratchet system that requires vortex-vortex interactions to work, in contrast with the individual vortex effects studied in conventional ratchet systems. By tuning the magnetic field and temperature, we are able to control the transition from a single vortex pinning regime to a region where collective effects become important and determine the range where the rectification effect is activated.

Experimental Study on Plasticity of Current-driven Vortex Lattices Interacting with Disorder in Bi2Sr2Ca1Cu2O8 Single Crystal

From the I-V characteristics for as-grown and irradiated Bi2Sr2CaCu2O8+δ single crystals at T=5K (i.e. T → 0) in a magnetic field applied parallel to c axis, we have seen two types of vortex dynamics above the depinning threshold, depending on the vortex-vortex interaction strength (λab/a0). For the as-grown sample, at a low field, the I-V curves show steps that clearly indicate a “fingerprint phenomenon” since they reflex the current dependence of the differential resistance rd(I). This can be ascribed to vortices flowing through uncorrelated channels for the highly defective lattice. As field sufficiently increase, these peaks merge to become broader ones indicating a crossover from filament type to braid river type. In contrast, in the irradiated sample, the pinning is found to be individual at low fields and collective when the vortex-vortex interactions are involved.

Superconductivity in La1.56Sr0.44CuO4/La2CuO4 Superlattices

Superlattices of the repeated structure La(1.56)Sr(0.44)CuO(4)/La(2)CuO(4) (LSCO-LCO), where none of the constituents is superconducting, show a superconducting transition of T_c \simeq 25 K. In order to elucidate the nature of the superconducting state we have performed a low-energy muSR study. By applying a magnetic field parallel (Meissner state) and perpendicular (vortex state) to the film planes, we could show that superconductivity is sheet like, resulting in a very anisotropic superconducting state. This result is consistent with a simple charge-transfer model, which takes into account the layered structure and the difference in the chemical potential between LCO and LSCO, as well as Sr interdiffusion. Using a pancake-vortex model we could estimate a strict upper limit of the London penetration depth to 380 nm in these superlattices. The temperature dependence of the muon depolarization rate in field cooling experiments is very similar to what is observed in intercalated BSCCO and suggests that vortex-vortex interaction is dominated by electromagnetic coupling but negligible Josephson interaction.

Thermal Depinning of Abrikosov Vortices in a Nb Polycrystalline Bulk Absorber for Gamma-Ray Superconducting Detector

The threshold temperature at which the thermal depinning of Abrikosov vortices starts to be pronounced, defines the upper temperature limit for secure operation of a gamma-ray superconducting detector based on Abrikosov vortices. Indeed, because of the flux creep phenomenon, unwanted spontaneous vortex jumps can take place concurrently with those resulting from the gamma-ray photon absorption, resulting in the appearance of dark counts. Low temperature magnetic force microscopy (MFM) was applied for the evaluation of the threshold temperature for a 0.3 mm thick Nb polycrystalline bulk absorber with dimensions of 5×5 mm2, which was chosen for the fabrication of Josephson tunnel junctions serving as vortex sensor element of the gamma-ray detector. Vortices were generated by cooling the sample to 4.3 K in a small magnetic field. A field of 0.1 mT was chosen in order to produce more than two vortices within the 7×7 μm2 scan area, but with sufficiently large inter-vortex spacing such that vortex-vortex interactions would be negligible. The threshold temperature associated with the thermal depinning of a single vortex was found to be 6.3 ± 0.2 K, whereas the threshold temperature associated with the thermal depinning of half of vortices was found to be 7.2 ± 0.2 K.

Genesis of Typhoon Nari (2001) from a mesoscale convective system

[1] In this study, the origin and genesis of Typhoon Nari (2001) as well as its erratic looping track, are examined using large-scale analysis, satellite observations, and a 4 day nested, cloud-resolving simulation with the finest grid size of 1.33 km. Observational analysis reveals that Nari could be traced 5 days back to a diurnally varying mesoscale convective system with growing cyclonic vorticity and relative humidity in the lower troposphere and that it evolved from a mesoscale convective vortex (MCV) as moving over a warm ocean under the influence of a subtropical high, a weak westerly baroclinic disturbance, an approaching-and-departing Typhoon Danas to the east, and the Kuroshio Current. Results show that the model reproduces the genesis, final intensity, looping track, and the general convective activity of Nari during the 4 day period. It also captures two deep subvortices at the eye-eyewall interface that are similar to those previously observed, a few spiral rainbands, and a midget storm size associated with Nari's relatively dry and stable environment. We find that (1) continuous convective overturning within the MCV stretches the low-level vorticity and moistens a deep mesoscale column that are both favorable for genesis; (2) Nari's genesis does not occur until after the passage of the baroclinic disturbance; (3) convective asymmetry induces a smaller-sized vortex circulation from the preexisting MCV; (4) the vortex-vortex interaction with Danas leads to Nari's looping track and temporal weakening; and (5) midlevel convergence associated with the subtropical high and Danas accounts for the generation of a nearly upright eyewall.

Nonuniform and coherent motion of superconducting vortices in the picometer-per-second regime

We investigated vortex dynamics in a single-crystal sample of type-II superconductor NbSe$_{2}$ using scanning tunneling microscopy at 4.2 K. The decay of the magnetic field at a few nT/s in our superconducting magnet induced the corresponding motion of vortices at a few pm/s. Starting with an initial magnetic field of 0.5 T, we continued to observe motion of vortices within a field of view of 400$\times$400 nm$^2$ subject to decay of the magnetic field over a week. Vortices moved collectively, and maintained triangular lattices due to strong vortex-vortex interactions during the motion. However, we observed two peculiar characteristics of vortex dynamics in this superconductor. First, the speed and direction of the vortex lattice motion were not uniform in time. Second, despite the non-uniform motion, we also found that there exists an energetically favored configuration of the moving vortices in the single-crystal sample of NbSe$_{2}$ based on the overlaid trajectories and their suppressed speeds. We model the system with weak bulk pinning, strong bulk pinning, and edge barrier effects.

Disordered chain model of cross tie wall spacing

We present a general analytical model for periodic chains of elastically coupled particles subject to thermal noise and quenched disorder. Our model estimates the variance in particle spacing in the long-time limit as a function of the strength of disorder and the deterministic coupling. We apply our theory to experimental results from magnetic cross tie domain wall studies. We extract a measure of the vortex-vortex interaction in the cross tie wall and relate this to the mean and variance in vortex-vortex spacing for a cross tie wall.

Conditions for nonmonotonic vortex interaction in two-band superconductors

We describe a semi-analytic approach to the two-band Ginzburg-Landau theory, which predicts the behavior of vortices in two-band superconductors. We show that the character of the short-range vortex-vortex interaction is determined by the sign of the normal domain - superconductor interface energy, in analogy with the conventional differentiation between type-I and type-II superconductors. However, we also show that the long-range interaction is determined by a modified Ginzburg-Landau parameter $\kappa^*$, different from the standard $\kappa$ of a bulk superconductor. This opens the possibility for non-monotonic vortex-vortex interaction, which is temperature-dependent, and can be further tuned by alterations of the material on the microscopic scale.

Vortex-vortex interaction in bulk superconductors: Ginzburg-Landau theory

The vortex-vortex interaction potential in bulk superconductors is calculated within the Ginzburg-Landau (GL) theory and is obtained from a numerical solution of a set of two coupled non-linear GL differential equations for the vector potential and the superconducting order parameter, where the merger of vortices into a giant vortex is allowed. Further, the interaction potentials between a vortex and a giant vortex and between a vortex and an antivortex are obtained for both type-I and type-II superconductors. Our numerical results agree asymptotically with the analytical expressions for large inter-vortex separations which are available in the literature. We propose new empirical expressions valid over the full interaction range, which are fitted to our numerical data for different values of the GL parameter.

Vortex Viscosity in Magnetic Superconductors Due to Radiation of Spin Waves

In type-II superconductors that contain a lattice of magnetic moments, vortices polarize the magnetic system inducing additional contributions to the vortex mass, vortex viscosity, and vortex-vortex interaction. Extra magnetic viscosity is caused by radiation of spin waves by a moving vortex. Like in the case of Cherenkov radiation, this effect has a characteristic threshold behavior and the resulting vortex viscosity may be comparable to the well-known Bardeen-Stephen contribution. The threshold behavior leads to an anomaly in the current-voltage characteristics, and a drop in dissipation for a current interval that is determined by the magnetic excitation spectrum.

Coupling effect diagnoses of quasi-stationary mesoscale vortex in Guangxi rainstorm process of China

The mesoscale weather system which affected the Guangxi flash-flood-producing rainstorm of China in June 2008 is a quasi-stationary mesoscale vortex. Its genesis and development is closely related to the coupling effects of weather systems in different scales and different latitudes. On the one hand, the coupling of synoptic scale high- and low-level jets provides the environmental conditions for development of vortices and vertical circulations in the mesoscale vortex; On the other hand, the coupling of waves in mid-latitude westerlies and perturbations in low-latitude warm-moist flow under the influence of complex terrain makes the mesoscale vortex circulations strengthened. With the piecewise potential vorticity (PV) inversion method, PV anomalies in different regions are analyzed; also the vortex-vortex interactions and vortex-background flow interactions are diagnosed. Thus, the reasons why the mesoscale is quasi-stationary at first, while developing and deepening later are indicated. Under the condition of coupling effects, the vertical motions accompanied with the mesoscale vortex can be diagnosed with the PV-ω inversion system based on the analysis of quasi-balanced flow.

Vortex clusters and multiquanta flux lattices in thin films of anisotropic superconductors

The distinctive features of equilibrium vortex structures in thin films of anisotropic superconductors in tilted magnetic fields are studied for the limits of moderate and strong anisotropy. The energetically favorable shape of isolated vortex lines is found in the framework of two particular models describing these limiting cases: London theory with an anisotropic mass tensor and London-type model for a stack of Josephson-decoupled superconducting layers. The increase in the field tilting is shown to result in qualitative changes in the vortex-vortex interaction potential: the balance between long-range attractive and repulsive forces occurs to be responsible for a formation of a minimum of the interaction potential vs the intervortex distance. This minimum appears to exist only for a certain restricted range of the vortex tilting angles which shrinks with the decrease in the system anisotropy parameter. 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 $M$ of flux quanta. Thus, the increase in the field tilting should be accompanied by the series of the phase transitions between the vortex lattices with different $M$.

Commensurability, jamming, and dynamics for vortices in funnel geometries

We use numerical simulations to examine vortex states and dynamics in periodic funnel geometries where a drive is applied in the easy flow direction. We show that this system exhibits a number of different commensurability effects when the vortex configurations match to both the periodicity of the array and the geometry of the funnels. The vortex configurations in this system are generally different from those observed for single isolated triangular superconducting samples due to the coupling of vortices in adjacent funnels. At certain matching fields, peaks in the critical current are absent due to the particular vortex configurations that occur at these fields. We find that the overall depinning force increases with increasing vortex density as a result of the enhanced vortex-vortex interactions caused by a crowding effect at the funnel tips. When a system becomes less mobile as a result of increased particle interactions, it is said to exhibit a jamming behavior. Under an applied drive we observe a series of elastic and plastic vortex flow phases which produce pronounced features such as jumps or dips in the transport curves. In all of the flow phases, only one vortex can pass through the funnel tip at a time due to the vortex-vortex repulsion forces. As a consequence of this constraint, we observe the remarkable result that the sum of the vortex velocities at a fixed drive remains nearly constant with increasing magnetic field B rather than increasing linearly. This result is similar to the behavior of sand in an hourglass. We also show how noise fluctuations can be used to distinguish the different flow phases. Our results should be readily generalizable to other systems of particles flowing in periodic funnel geometries, such as colloids or Wigner crystals.

Computational Investigation of Microscale Coaxial-Rotor Aerodynamics in Hover

In this work, a compressible Reynolds-averaged Navier-Stokes solver is used to investigate the aerodynamics of a microscale coaxial-rotor configuration in hover, to evaluate the predictive capability of the computational approach and to characterize the unsteadiness in the aerodynamic flowfield of the microscale coaxial systems. The overall performance is well-predicted for a range of rpm and rotor spacing. As the rotor spacing increases, the top-rotor thrust increases and the bottom-rotor thrust decreases, while the total thrust remains fairly constant. The thrusts approach a constant value at very large rotor spacing. Top rotor contributes about 55 % of the total thrust at smaller rotor spacing, which increases to about 58% at the largest rotor separation. The interaction between the rotor systems is seen to generate significant impulses in the instantaneous thrust and power. Unsteadiness is mainly caused due to blade loading and wake effect. Additional high-frequency unsteadiness was also seen due to shedding near the trailing edge. The phasing of the top vortex impingement upon the bottom rotor plays a significant role in the amount of unsteadiness for the bottom rotor. Interaction of the top-rotor tip vortex and inboard sheet with the bottom rotor results in a highly three-dimensional shedding on the upper surface of the blade in the outboard region and a two-dimensional shedding on the lower surface at the inboard portion of the blade. The wake of the top rotor contracts faster compared with that of the bottom rotor because of the vortex-vortex interaction. Further, the top-rotor wake convects vertically down at a faster rate due to increased inflow.

Filamentary flow of vortices in aBi2Sr2Ca1Cu2O8+δsingle crystal

Using micro-bridge technique, we have studied the vortex dynamics in a very low temperature region (i.e. T/Tc -> 0) of the B-T phase diagram of Bi_2Sr_2Ca_1Cu_2O_{8+\delta} single crystal. We distinguish two types of vortex dynamics near the depinning threshold depending on the magnitude of the vortex-vortex interactions. For 0.01 <= \mu_0H <= 1T, we show that current-voltage characteristics (I-V) are strongly dependent on the history of magnetic field and current cycling. The sharp peak, so called "peak effect" (PE), observed in \mu_0H-Ic curve is due to a metastable state which can be removed after current cycling. At low field, I-V curves exhibit steps which clearly enligth a "fingerprint phenomenon" as it can be seen the current dependence of the differential resistance Rd = dV/dI. We associate this to vortices flow through uncorrelated channels for the highly defective lattice. Indeed, as field sufficiently increase, these peaks merge giving broader ones indicating a crossover from filamentaty strings to braid river like in which vortex-vortex interactions becomes significant. As confirmed by the discontinuity in the critical exponent value \beta determined in the vicinity of the threshold current using the power-law scaling V (I-Ic)^\beta with a crossover from \beta = 2.2 to \beta = 1.2. The strong vortex correlation along the c-axis has been clearly demonstrated using the dc-flux-transformer geometry for transport measurements which confirms the pseudo-2D behaviour of the FLL. Our transport studies are in good agreement with recent simulations results of 2D elastic objects driven by repulsive interactions through a random pinning potential.