Interstitial Vortices Research Articles

Experimental and simulation study of pinning phenomena in superconductors with regular composite pinning arrays

Pinning phenomena were investigated in the superconducting Nb thin film with composite hexagonal arrays. The composite pinning arrays were consisting of two kinds of pinning sites with different pinning sizes. The smaller pinning defects were added to the center of every honeycomb pinning array to observe the configuration of the vortices, comparing to the periodic triangular and honeycomb arrays. The film with this kind of composite array can be regarded as a transition between the films with triangular array and honeycomb array. The critical current as a function of magnetic field for four samples were measured. Regular 150 Oe interval of the matching fields for the triangular arrays was found, while for the honeycomb arrays, the interstitial vortices were caged at the center of every honeycomb array, causing 50 Oe interval of the matching fields. For the samples with composite arrays, the 100 Oe or 50 Oe intervals of matching fields correspond to every larger or smaller pinning site capturing one more vortex, respectively. We found that the relative pinning strength of the large pinning sites is greater than that of the small ones. We conducted the simulations based on the time dependent Ginzburg-Landau theory to confirm that the interstitial vortices did exist in the honeycomb arrays which caused the various intervals between the matching fields.

A superconducting/magnetic hybrid rectifier based on Fe single-crystal nanocentres: role of magnetic and geometric asymmetries

Vortex lattice motion driven by alternating forces on asymmetric pinning potentials generates a net flow of vortices. This rectifier (ratchet) effect is studied in hybrid samples fabricated with arrays of Fe single-crystal nanotriangles embedded in Nb films. In these samples two different asymmetric potentials generate the ratchet effect: (i) potentials with geometric asymmetry and (ii) potentials with magnetic asymmetry. The asymmetry of the geometric potential cannot be manipulated, but the asymmetry of the magnetic potential can be tailored. In geometric ratchet interstitial vortices play a crucial role and they permit tuning the output voltage polarity. In magnetic ratchet the output voltage amplitude can be controlled by tailoring the magnetic stray field configurations due to different magnetic remanent states of the Fe single-crystal nanostructures. These configurations are modified by changing the direction of the saturating applied field and also by using different orientations of the Fe magnetocrystalline easy axes within the triangles. When both mechanisms coexist, the geometric potential governs the rectifier effect behaviour.

Ginzburg–Landau Study of Superconductor with Regular Pinning Array

The vortex distributions and dynamics in superconductors with triangular and honeycomb pinning arrays are investigated by numerical simulation of the two- dimensional (2-D) time-dependent Ginzburg–Landau equations. Periodic boundary conditions are implemented through specific gauge transformations under lattice translations. We model the pinning sites as holes. The simulation results at different magnetic fields are presented. For film with regular triangular pinning array, the vortices are all captured within the holes for a wide range of magnetic fields. For film with regular honeycomb pinning array, the interstitial vortices appear at relatively low magnetic fields. With an increase of magnetic field, the new vortices may enter the holes again and keep the number of vortices at the interstitial positions unchanged. These results confirm our explanations of the experimental results we obtained earlier.

Depinning of Two-Dimensional Vortex System with Square Pinning Array at the Second Matching Field

Depinning of a two-dimensional vortex system at the second matching field B=2Bϕ in the presence of square pinning array was studied by molecular dynamics simulations. The annealed ground structures and depinning properties are found to be dependent on pinning strength. For strong pinning, we find a two-step depinning transition with a lower depinning force Fc1 and a higher one Fc2. At Fc1 only the interstitial vortices start to move, while at Fc2 the vortices at pinning sites are depinned and all vortices move.

Current carrying vortex crystals

Abrikosov vortices in a type-II superconducting film subjected to strong magnetic field B with periodic array of nanoholes of the density npin form sometimes a vortex crystal, even when they are driven by a transport current. It is shown numerically that the crystal melting and transition to the resistive state occurs as a coherent depinning of the single vortex dislocations. For a system with interstitial vortices, f = B/φ0npin > 1, the mechanism of depinning depends on the current direction with respect to the pinning array. It was found that slightly above the critical current trajectories of moving vortices are not straight, but rather acquire a snake - like shape enveloping the system of pins. In contrast to the matching field case, f = 1, the transition to a resistive state is not coherent and is developing through formation of the “snake - like” vortex trajectories. It is pointed out that the depinning is closely associated with the appearance of a strongly varying electric field. We calculated the electric fields accompanying vortex crystal melting and found the voltage-current characteristics. When the pinning array is made random, the critical current is reduced.

Reconfiguration and hysteresis in superconducting Nb film with honeycomb arrays

Superconducting Nb films with honeycomb array of holes are studied using transport measurements. The oscillating magneto-resistance curves are observed up to large flux density. Two types of resistance minima with different field intervals are observed, indicating the reconfiguration of the overall flux lattice from honeycomb to triangular arrangement. Moreover, hysteretic effects are found in a very large field span from H = 2H1 to H = 8.5H1. It is revealed that the hysteresis is related to the presence of interstitial vortices.

Critical Currents and Melting Temperature of a Two-Dimensional Vortex Lattice with Periodic Pinning

The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two-dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagome. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for the hexagonal pinning lattice and anisotropic for both pinning arrays. This anisotropy is stronger with temperature for the hexagonal array. For the Kagome pinning lattice, our analysis shows a multi stage phase melting; that is, as we increase the temperature, each different dynamic phase melts before reaching the melting temperature. Both the melting temperature and critical currents are larger for the hexagonal lattice, indicating the role for the interstitial vortices in decreasing the pinning strength.

Interstitial vortex in superconducting film with periodic hole arrays

The response of superconducting Nb films with a diluted triangular and square array of holes to a perpendicular magnetic field are investigated. Due to small edge-to-edge separation of the holes, the patterned films are similar to multi-connected superconducting islands. Two regions in the magnetoresistance R(H) curves can be identified according to the field intervals of the resistance minima. Moreover, in between these two regions, variation of the minima spacing was observed. Our results provide strong evidence of the coexistence of interstitial vortices in the islands and fluxoids in the holes.

Crossover behaviors in magnetoresistance oscillations for Nb thin film with rectangular arrays of antidots

Superconducting Nb thin films with rectangular arrays of submicron antidots (holes) have been systemically investigated by transport measurements. A series of crossover behaviors is found in magnetoresistance oscillations, corresponding to three different superconducting states: the wire network-like state, the interstitial vortex state and the single-loop–like state. These states are identified by the field intervals and hysteretic effect. The crossover fields between them are found to be both temperature and geometry dependent. Furthermore, in dense arrays, the saturation number is distinctly larger than the theoretical calculation for a single insulating inclusion. Our results indicate that in the process of magnetic field penetration into nanostructured superconductors, the order parameters are strongly modulated and finally localized near the edges, resulting in changes of oscillation modes.

Abnormal magnetoresistance behavior in Nb thin films with rectangular arrays of antidots

Magnetoresistance in superconducting Nb films perforated with rectangular arrays of antidots (holes) is investigated at various temperatures and currents. Normally, the magnetoresistance increases with the increasing magnetic field. In this paper, we report a reverse behavior in a certain range of high fields after vortex reconfiguration transition, where the resistances at non-matching fields are smaller than those in the low field regime. This phenomenon is due to a strong caging effect, in which the interstitial vortices are trapped among the pinned multiquanta vortices. This effect is temperature and current dependent.

Vortex interaction enhanced saturation number and caging effect in a superconducting film with a honeycomb array of nanoscale holes

The electrical transport properties of a MoGe thin film with a honeycomb array of nanoscale holes are investigated. The critical current of the system shows nonmatching anomalies as a function of applied magnetic field, enabling us to distinguish between multiquanta vortices trapped in the holes and interstitial vortices located between the holes. The number of vortices trapped in each hole is found to be larger than the saturation number predicted for an isolated hole and shows a nonlinear field dependence, leading to the caging effect as predicted from the Ginzburg-Landau (GL) theory. Our experimental results are supplemented by numerical simulations based on the GL theory.

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.

Bitter decoration of vortex patterns in superconducting Nb films with random, triangular, and Penrose arrays of antidots

We imaged Abrikosov vortex patterns in thin Nb films with random, periodic (triangular), and quasiperiodic (Penrose) arrays of antidots. Vortex positions were visualized by Bitter decoration for a range of applied fields $B$, antidot radii $r$, and densities ${n}_{p}$ after field-cooling through the transition temperature ${T}_{c}$ to a base temperature $T\ensuremath{\approx}2\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The observed vortex patterns correspond to snapshots of vortex positions at the time of decoration. The effectiveness of antidots as artificial pinning sites for vortices is found to be sensitive to several factors: array geometry, antidot size and density, and applied field. Overall, the triangular lattice provides the most effective pinning landscape, with antidots trapping the highest proportion of vortices, but for a wide range of parameters the Penrose lattice is equally effective. For a quantitative analysis, we determined the occupation number $n$ (average number of vortices trapped per antidot) from each image. This revealed a significantly more complicated dependence of antidot occupation on applied field and/or antidot density than that predicted by simple models considering pinning by an isolated antidot. In particular, upon increasing the antidot density ${n}_{p}$, we find a marked increase in $n$ for triangular arrays, which we attribute to the additional repulsion from interstitial vortices, pushing more vortices into antidots with decreasing antidot separation. This effect is also present but less pronounced for Penrose arrays, which can be explained by the variation of antidot spacing inherent to the Penrose geometry and accordingly more options for accommodating interstitial vortices.

Vortex ratchet reversal: Role of interstitial vortices

Triangular arrays of Ni nanotriangles embedded in superconducting Nb films exhibit unexpected dynamical vortex effects. Collective pinning with a vortex lattice configuration different from the expected fundamental triangular "Abrikosov state" is found. The vortex motion which prevails against the triangular periodic potential is produced by channelling effects between triangles. Interstitial vortices coexisting with pinned vortices in this asymmetric potential, lead to ratchet reversal, i.e. a DC output voltage which changes sign with the amplitude of an applied alternating drive current. In this landscape, ratchet reversal is always observed at all magnetic fields (all numbers of vortices) and at different temperatures. The ratchet reversal is unambiguously connected to the presence of two locations for the vortices: interstitial and above the artificial pinning sites.

Experimental and simulation study of missing matching peaks in Nb thin films with square pinning arrays

Square arrays of circular pinning centers of various diameters were patterned in Nb thin films to explore their vortex pinning behavior. Periodic critical current matching peaks and some “missing peaks” were observed in magnetotransport measurements. The larger the diameter of the pinning centers, the higher the index of the missing matching fields observed. This phenomenon is explained by molecular dynamics simulations and is caused by the interaction between interstitial vortices and vortices occupying the pinning centers.

Hall Effect due to channeled pinning potential in Nb thin films

We have studied the Magnetoresistance and Hall Effect in Nb superconducting thin films with triangular arrays of holes. Three different arrays of defects have been prepared with different orientations with respect to the current. Because vortex dynamics in the mixed state in type-II superconductors is strongly influenced by the pinning centers, a channeled pinning landscape is formed by the pinned vortices. It is suggested that the motion of interstitial vortices has great influence by the channel. When vortices propagate through these arrays, both the longitudinal and transversal voltages show cusp-like anomalies at matching fields. Vortices can be guided by the channel formed between pinned vortices. The longitudinal voltages are the same when there is a sign change of magnetic field. The longitudinal and transversal Hall voltages are dependent on the rotating angle of the arrays.

Transport current carrying superconducting film with periodic pinning array under strong magnetic fields

The transport current carrying dissipative (flux flow) and dissipationless (pinned) vortex configurations and their dynamics are investigated numerically in the framework of the time-dependent Ginzburg-Landau approach. Assuming that magnetic induction is nearly uniform, the model is generalized to include strong inhomogeneous electric fields. Hexagonal array nanoholes of the size of coherence length and density ${n}_{\text{pin}}$ was considered for various filling factors [defined as $f=B/({\ensuremath{\Phi}}_{0}{n}_{\text{pin}})$]. The vortex depinning is closely associated with the appearance of a strongly varying electric field. For the matching field, $f=1$, the critical current is maximal and the transition to the resistive state occurs as a coherent depinning of the entire vortex lattice. For a system with interstitial vortices, $fg1$, the mechanism of depinning depends on the current direction with respect to the pinning array. There are two qualitatively distinct geometries: the obstacle and channel geometries. In the obstacle geometry lines of interstitial vortices are blocked by strongly pinned vortices, while in the channel geometry the lines move unimpeded confined in channels. It was found that slightly above the critical current the trajectories of the moving vortices are not straight, but rather acquire a snakelike shape enveloping the system of pins. In contrast to $ f=1$, the transition to a resistive state is not coherent and is going through formation of ``snakelike'' vortex trajectories. The critical current in the obstacle geometry is significantly larger than in the channel one.

Intermediate vortex states in nanoscale anti-dots and mesoscopic superconductors

We have fabricated anti-dots array in Nb and NbN, and high-Tc superconductor Bi2Sr2CaCu2Oy (Bi-2212), and have measured the flow-resistance of vortices perpendicular to the array and magnetic field. We could produce a variety of vortex-matching effect; the usual and the fractional matching. In low-Tc superconductors, the usual matching effect shows "dips" in the flow resistance at the matching field. However, it shows "humps" at higher matching magnetic fields to be related to the formation of giant vortices and/or interstitial vortices. In Bi-2212, the matching effect is closely related to the first order transition of vortex lattice melting in the pristine samples in the presence of the anti-dot arrays. We also have measured the vortex state in mesoscopic type-I superconductor of In. This includes the observation of topological hysteresis with a signature of occurrence in different critical fields during vortex entry and exit. We will show the existence of a metastable configuration of vortices depending on the recipes to access them, and demonstrate the manifestation of superheating and supercooling of superconducting and normal states, respectively, across the superconducting transition.

Electrodynamics of type-II superconductor with periodic pinning array

Static and dynamic distribution of the superconducting condensate order parameters and current density is studied by numerical simulation of the 2D time-dependent Ginzburg–Landau equations. The vortex flux lattice in layered type-II superconductors under magnetic field above the lower critical field is described by the order parameters. Moreover, the pinning effect has been considered in this work. The Abrikosov lattice which is hexagonal in the static case is deformed due to the size of pinning centers. The dynamical order parameters distribution shows that the vortex transport (flux flow) is conducted via diffusive motion of the so-called interstitial vortices. The trajectories for interstitial vortices with different sizes of pinning centers are shown.

Multi-vortex versus interstitial vortices scenario in superconducting antidot arrays

In superconducting thin films, engineered lattice of antidots (holes) act as an array of columnar pinning sites for the vortices and thus lead to vortex matching phenomena at commensurate fields guided by the lattice spacing. The strength and nature of vortex pinning is determined by the geometrical characteristics of the antidot lattice (such as the lattice spacing a0, antidot diameter d, lattice symmetry, and orientation) along with the characteristic length scales of the superconducting thin films, viz., the coherence length (ξ) and the penetration depth (λ). There are at least two competing scenarios: (i) multiple vortices sit on each of the antidots at a higher matching period and (ii) there is nucleation of vortices at the interstitial sites at higher matching periods. Furthermore, it is also possible for the nucleated interstitial vortices to reorder under suitable conditions. We present our experimental results on NbN antidot arrays in the light of the above scenarios.