Recent experiments [I.V. Grigorieva et al., Phys. Rev. Lett. 96, 077005 (2006)] on visualization of vortices using the Bitter decoration technique revealed vortex shells in mesoscopic superconducting Nb disks containing up to L=40 vortices. Some of the found configurations did not agree with those predicted theoretically. We show here that this discrepancy can be traced back to the larger disks with radii R ~ 1 to 2.5μm, i.e., R ~ 50-100ξ(0) used in the experiment, while in previous theoretical studies vortex states with vorticity L < 40 were analyzed for smaller disks with R ~ 5-20ξ(0). The present analysis is done for thin disks (mesoscopic regime) and for thick (macroscopic) disks where the London screening is taken into account. We found that the radius of the superconducting disk has a pronounced influence on the vortex configuration in contrast to, e.g., the case of parabolic confined charged particles. The missing vortex configurations and the region of their stability are found, which are in agreement with those observed in the experiment.
We investigated the Abrikosov vortex lattice (VL) of a pure Niobium single crystal with the muon spin rotation (μSR) technique. Analysis of the μSR data in the framework of the BCS-Gor'kov theory allowed us to determine microscopic parameters and the limitations of the theory. With decreasing temperature the field variation around the vortex cores deviates substantially from the predictions of the Ginzburg-Landau theory and adopts a pronounced conical shape. This is evidence of partial diffraction of Cooper pairs on the VL predicted by Delrieu for clean superconductors.
We report measurements of voltage noise due to vortex motion in Niobium, a conventional low-Tc superconductor. A coherent oscillation leading to narrow band noise (NBN) is evidenced. Its characteristic frequency is a linear function of the overcritical transport current in the flux-flow regime, and hence scales as the main velocity of the vortex flow. The associated length scale is not the intervortex distance but the width of the sample, indicating temporal coherence at a large scale. NBN is also observed in the non linear part of the V(I) at the onset of depinning, in apparent disagreement w…
We have investigated the intermediate mixed state of a superconducting niobium sample by Very Small Angle Neutron Scattering.We show that this state is stabilized through a sequence where a regular vortex lattice appears, which then coexists with vortex clusters before vanishing at low temperature. Vortices in clusters have a constant periodicity regardless of the applied field, exhibit a temperature dependence close to the one of the penetration depth. The clusters disappear in the high temperature limit. All the results agree with an explanation in terms of vortex attraction due non local ef…
In the intermediate mixed state (IMS) of type-II/1 superconductors, vortex lattice (VL) and Meissner state domains coexist due to a partially attractive vortex interaction. Using a neutron-based multiscale approach combined with magnetization measurements, we study the continuous decomposition of a homogeneous VL into increasingly dense domains in the IMS in bulk niobium samples of varying purity. We find a universal temperature dependence of the vortex spacing, closely related to the London penetration depth and independent of the external magnetic field. The rearrangement of vortices occurs …
The field distribution in the vortex lattice of a pure niobium single crystal with an external field applied along a three-fold axis has been investigated by the transverse-field muon-spin-rotation (TF-$μ$SR) technique over a wide range of temperatures and fields. The experimental data have been analyzed with the Delrieu's solution for the form factor supplemented by phenomenological formulas for the parameters. This has enabled us to experimentally establish the temperatures and fields for the Delrieu's, Ginzburg-Landau's, and Klein's regions of the vortex lattice. Using the numerical solutio…
Superconducting vortex lattices, glasses and liquids attract great interest as model systems of crystallization and as a source of microscopic information of the nature of superconductivity. We report for the first time direct microscopic measurements of the vortex lattice tilt modulus c44 in ultra-pure niobium using time-resolved small angle neutron scattering. Besides a general trend to faster vortex lattice dynamics for increasing temperatures we observe a dramatic changeover of the relaxation process associated with the non-trivial vortex lattice morphology in the intermediate mixed state.…
In 1993 Tang proposed [1] that vortex avalanches should produce a self organized critical state in superconductors, but conclusive evidence for this has heretofore been lacking. In the present paper, we report extensive micro-Hall probe data from the vortex dynamics in superconducting niobium, where a broad distribution of avalanche sizes scaling as a power-law for more than two decades is found. The measurements are combined with magneto-optical imaging, and show that over a widely varying magnetic landscape the scaling behaviour does not change, hence establishing that the dynamics of superc…
A thermodynamically stable vortex-antivortex pattern has been revealed in mesoscopic type I superconducting triangles, contrary to type II superconductors where similar patterns are unstable. The stable vortex-antivortex "molecule" appears due to the interplay between two factors: a repulsive vortex-antivortex interaction in type I superconductors and the vortex confinement in the triangle.
Solving numerically the 3D non linear Ginzburg-Landau (GL) equations, we study equilibrium and nonequilibrium phase transitions between different superconducting states of mesoscopic disks which are thinner than the coherence length and the penetration depth. We have found a smooth transition from a multi-vortex superconducting state to a giant vortex state with increasing both the disk thickness and the magnetic field. A vortex phase diagram is obtained which shows, as function of the magnetic field, a re-entrant behavior between the multi-vortex and the giant vortex state.
The discrete shell structure of vortex matter strongly influences the flux dynamics in mesoscopic superconducting Corbino disks. While the dynamical behavior is well understood in large and in very small disks, in the intermediate-size regime it occurs to be much more complex and unusual, due to (in)commensurability between the vortex shells. We demonstrate unconventional vortex dynamics (inversion of shell velocities with respect to the gradient driving force) and angular melting (propagating from the boundary where the shear stress is minimum, towards the center) in mesoscopic Corbino disks.
Using multi-component Ginzburg-Landau simulations, we show a plethora of vortex states possible in mesoscopic three-band superconductors. We find that mesoscopic confinement stabilizes chiral states, with non-trivial phase differences between the band-condensates, as the ground state of the system. As a consequence, we report the broken-symmetry vortex states, the chiral states where vortex cores in different band condensates do not coincide (split-core vortices), as well as fractional vortex states with broken time-reversal symmetry.
The morphology of the superconducting flux line lattice (FLL) of Nb comprises gradual variations with various lock-in transitions and symmetry breaking rotations. We report a comprehensive small-angle neutron scattering study of the FLL in an ultra-pure single crystal of Nb as a function of the orientation of the applied magnetic field. We attribute the general morphology of the FLL and its orientation to three dominant mechanisms. First, non-local contributions, second, the transition between open and closed Fermi surface sheets and, third, the intermediate mixed state between the Meissner an…
We study the magnetoconductance fluctuations of mesoscopic normal-metal/superconductor (NS) samples consisting of a gold-wire in contact with a niobium film. The magnetic field strength is varied over a wide range, including values that are larger than the upper critical field B_c2 of niobium. In agreement with recent theoretical predictions we find that in the NS sample the rms of the conductance fluctuations (CF) is by a factor of 2.8 +/- 0.4 larger than in the high field regime where the entire system is driven normal conducting. Further characteristics of the CF are discussed.
We analyze theoretically and experimentally vortex configurations in mesoscopic superconducting squares. Our theoretical approach is based on the analytical solution of the London equation using Green's-function method. The potential-energy landscape found for each vortex configuration is then used in Langevin-type molecular-dynamics simulations to obtain stable vortex configurations. Metastable states and transitions between them and the ground state are analyzed. We present our results of the first direct visualization of vortex patterns in micrometer-sized Nb squares, using the Bitter decor…
The dense vortex matter structure and associated magnetization are calculated for type-II superconducting mesoscopic disks. The magnetization exhibits generically first-order phase transitions as the number of vortices changes by one and presents two well-defined regimes: A non-monotonous evolution of the magnitude of the magnetization jumps signals the presence of a vortex glass structure which is separated by a second-order phase transition at $H_{c2}$ from a condensed state of vortices (giant vortex) where the magnitude of the jumps changes monotonously. We compare our results with Hall mag…
The nonlinear Ginzburg-Landau equations are solved numerically in order to investigate the vortex structure in thin superconducting disks of arbitrary shape. Depending on the size of the system and the strength of the applied magnetic field giant vortex, multi-vortex and a combination of both of them are found. The saddle points in the energy landscape are identified from which we obtain the energy barriers for flux penetration and expulsion.
We investigate how the geometrical symmetry affects the penetration and arrangement of vortices in mesoscopic superconductors using self-consistent Bogoliubov-de Gennes equations. We find that the entrance of the vortex happens when the current density at the hot spots reaches the depairing current density. Through determining the spatial distribution of hot spots, the geometrical symmetry of the superconducting sample influences the nucleation and entrance of vortices. Our results propose one possible experimental approach to control and manipulate the quantum states of mesoscopic superconduc…
Response of a mesoscopic superconducting disk to perpendicular magnetic fields is studied by using the multiple-small-tunnel-junction method, in which transport properties of several small tunnel junctions attached to the disk are measured simultaneously. This allows us for the first experimental distinction between the giant vortex states and multivortex states. Moreover, we experimentally find magnetic field induced rearrangement and combination of vortices. The experimental results are well reproduced in numerical results based on the nonlinear Ginzburg-Landau theory.
There seems to be a one to one correspondence between the phases of atomic and molecular matter (AMOM) and vortex matter (VM) in superfluids and superconductors. Crystals, liquids and glasses have been experimentally observed in both AMOM and VM. Here, we propose a vortex quasi-crystal state which can be stabilized due to boundary and surface energy effects for samples of special shapes and sizes. For finite sized pentagonal samples, it is proposed that a phase transition between a vortex crystal and a vortex quasi-crystal occurs as a function of magnetic field and temperature as the sample si…
The electronic structure of the giant vortex states in a mesoscopic superconducting disk is studied in a dirty limit using the Usadel approach. The local density of states profiles are shown to be strongly affected by the effect of quasiparticle (QP) tunneling between the states localized in the vortex core and the ones bound to the sample edge. Decreasing temperature leads to a crossover between the edge-dominated and core-dominated regimes in the magnetic field dependence of the tunneling conductance. This crossover is discussed in the context of the efficiency of quasiparticle cooling by th…
Rectangular pinning arrays of Ni dots define a potential landscape for vortex motion in Nb films. Magnetotransport experiments in which two in-plane orthogonal electrical currents are injected simultaneously allow selecting the direction and magnitude of the Lorentz force on the vortex-lattice, thus providing the angular dependence of the vortex motion. The background dissipation depends on angle at low magnetic fields, which is progressively smeared out with increasing field. The periodic potential locks in the vortex motion along channeling directions. Because of this, vortex-lattice directi…
We demonstrate an efficient numerical method for obtaining unique solutions to the Eilenberger equation for a mesoscopic or nanoscale superconductor. In particular, we calculate the local density of states of a circular d-wave island containing a single vortex. The "vortex shadow" effect is found to strongly depend on the quasiparticle energy in such small systems. We show how to construct by geometry quasiparticle trajectories confined in a finite-size system with specular reflections at the boundary, and discuss the stability of the numerical solutions even in the case of vanishing order par…
A numerical scheme to study the mixed states in a mesoscopic type-II superconducting cylinder is described. Steady-state configurations and transient behavior of the magnetic vortices for various values of the applied magnetic field H are presented. Transitions between different multi-vortex states as H is changed is demonstrated by contour plots and jumps in the B vs H plot. Evolving a uniformly-superconducting initial state using the simplest set of relaxation equations shows that the system passes through nearly metastable intermediate configurations, while seeking the final minimum-energy,…
The experimental investigation of the $I_c(B)$--$T_c(B)$ phase boundary of superconducting niobium films with large area quasihexagonal hole arrays is reported. The hole arrays were patterned with microsphere photolithography. We investigate the perforated niobium films by means of electrical directed current transport measurements close to the transition temperature $T_c$ in perpendicularly applied magnetic fields. We find pronounced modulations of the critcal current with applied magnetic field, which we interpret as a consequence of commensurable states between the Abrikosov vortex lattice …
We study geometrical confinement effects in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8 +δ}$ mesoscopic vortex-matter with edge-to-surface ratio of $7-12$%. Samples have in-plane square and circular edges, 30\,$μ$m widths, and $\sim 2\,μ$m thickness. Direct vortex imaging reveals the compact planes of the structure align with the sample edge by introducing topological defects. The defects density is larger for circular than for square edges. Molecular dynamics simulations suggest this density is not an out-of-equilibrium property but rather determined by the geometrical confinement.
The conformal mapping method is used to study the problem of flux line interaction with surface cavities having cylindrical profile and characteristic size much less than the penetration length, i.e, within mesoscopic scale. It is shown that the metastable states are achieved when the dimensions of the surface irregularities do not exceed the coherence length. Our study shows that the surface barrier may vanished at some weak point at which the surface irregularities have mesoscopic scales. On the other hand, the surface barrier is completely disappeared when the surface defects size is more g…
In this work we solved the time-dependent Ginzburg-Landau equations, TDGL, to simulate two superconducting systems with different lateral sizes and with an antidot inserted in the center. Then, by cycling the external magnetic field, the creation and annihilation dynamics of a vortex-antivortex pair was studied as well as the range of temperatures for which such processes could occur. We verified that in the annihilation process both vortex and antivortex acquire an elongated format while an accelerated motion takes place.
By using the full 3D generalized time dependent Ginzbug-Landau equation we study a long superconducting film of finite width and thickness under an applied transport current. We show that, for sufficiently large thickness, the vortices and the antivortices become curved before they annihilate each other. As they approach the center of the sample, their ends combine, producing a single closed vortex. We also determine the critical values of the thickness for which the closed vortex sets in for different values of the Ginzburg-Ladau parameter. Finally, we propose a model of how to detect a close…
The dynamics of the annihilation of a vortex-antivortex pair is investigated. The pair is activated magnetically during the run of a simulated hysteresis loop on a square mesoscopic superconducting cylinder with an antidot inserted at its center. We study the nucleation of vortices and antivortices by first increasing the magnetic field, applied parallel to the axis of the sample, from zero until the first vortex is created. A further increase of the field pulls the vortex in, until it reaches the antidot. As the polarity of the field is reversed, an antivortex enters the scene, travels toward…
We describe an experimental protocol to characterize magnetic field dependent microwave losses in superconducting niobium microstrip resonators. Our approach provides a unified view that covers two well-known magnetic field dependent loss mechanisms: quasiparticle generation and vortex motion. We find that quasiparticle generation is the dominant loss mechanism for parallel magnetic fields. For perpendicular fields, the dominant loss mechanism is vortex motion or switches from quasiparticle generation to vortex motion, depending on cooling procedures. In particular, we introduce a plot of the …
The vortex states in a thin mesoscopic disk are investigated within the phenomenological Ginzburg-Landau theory in the presence of different ''model'' magnetic field profiles with zero average field which may result from a ferromagnetic disk or circulating currents in a loop near the superconductor. We calculated the dependences of both the ground and metastable states on the magnitude and shape of the magnetic field profile for different values of the order parameter angular moment, i.e. the vorticity. The regions of existence of the multi-vortex state and the giant vortex state are found. We…
Applying the London theory we study curved vortices produced by an external current near and parallel to the surface of a type II superconductor. By minimizing the energy functional we find the contour describing the hard core of the flux line, and predict the threshold current for entrance of the first vortex. We assume that the vortex entrance is allowed due to surface defects, despite the Bean-Livingston barrier. Compared to the usual situation with a homogeneous magnetic field, the main effect of the present geometry is that larger magnetic fields can be applied locally before vortices ent…
A micron sized single crystal of the superconductor BSCCO was studied using silicon mechanical micro-oscillators at various tilt angles of the dc magnetic field with respect to the c axis of the sample. Different phases of the vortex matter were detected by measuring changes in the value and sign of the oscillator resonant frequency variation with temperature. We could explain the change in the sign of this variation at high temperatures as the transition from the 2D liquid of decoupled pancakes to a reversible 3D vortex lattice. The data indicates that this transition only depends on the magn…
We solve the Ginzburg-Landau equation (GLE) for the mesoscopic superconducting thin film of the square shape in the magnetic field for the wide range of the Ginzburg-Landau parameter 0.05< kappa. We focus on the region of the field where formation of the antivortex has been reported previously. We found that the phase with the antivortex exists in the broad range of parameters. When the coherence length decreases the topological phase transition to the phase with the same total vorticity and a reduced symmetry takes place. The giant vortex with the vorticity m=3 is found to be unstable for any…
Usually, the measurements of electronic and magnetic properties of superconducting samples are carried out under a constant temperature bath. On the other hand, thermal gradients induce local variation of the superconducting order parameter, and the vortex dynamics can present interesting behaviors. In this work, we solved the time-dependent Ginzburg-Landau equations simulating samples under two different thermal gradients, and considering two values of the Ginzburg-Landau parameter, \k{appa}. We find out that both parameters, i.e., \k{appa} and thermal gradients, play an important role on the…
In mesoscopic superconducting disks vortices form shell structures as recently observed in Nb disks. We study the dynamics of such vortices, driven by an external current I_0, in a Corbino setup. At very low I_0, the system exhibits rigid body rotation while at some critical current I_c,i vortex shells rotate separately with angular velocities omega_i. This critical current I_c,i has a remarkable non-monotonous dependence on the applied magnetic field which is due to a dynamically-induced structural transition with a rearrangement of vortices over the shells similar to the Coster-Kronig transi…
Symmetry-induced vortex-antivortex configurations in superconducting squares and triangles were predicted earlier; yet, they have not been resolved in experiment up to date. Namely, with vortex-antivortex states being highly unstable with respect to defects and temperature fluctuations, it is very unlikely that samples can be fabricated with the needed quality. Here we show how these drawbacks can be overcome by strategically placed nanoholes in the sample. As a result, (i) the actual shape of the sample becomes far less important, (ii) the stability of the vortex-antivortex configurations in …
Numerical calculations on a mesoscopic ring of a type II superconductor in the London limit suggest that an Abrikosov vortex can be trapped in such a structure above a critical magnetic field and generate a phase shift in the magnetoresistance oscillations. We prepared submicron-sized superconducting loops of single-crystal, type II superconductor NbSe$_2$ and measured magnetoresistance oscillations resulting from vortices crossing the loops. The free energy barrier for vortex crossing determines the crossing rate and is periodically modulated by the external magnetic flux threading the loop. …
Our study sample is a superconducting bi-dimensional octagon with different boundary conditions immersed in a magnetic external field H. The boundary conditions are simulated by considering different values of the deGennes extrapolation length b on different surfaces of the sample. Our investigation was carried out by solving the two-band time dependent Ginzburg-Landau equations (TB-TDGL). We analyzed the superconducting electron density and the magnetization curves as functions of H and temperature T in zero field cooling and in zero field cooling processes for different values of b and size …
The giant vortex states of a multiply connected superconductor, with radius comparable to the penetration depth and the coherence length, are theoretically investigated based on the nonlinear Ginzburg-Landau theory, in which the induced magnetic field by the super-currents is accurately taken into account. The solutions of Ginzburg-Landau equations are found to be actually independent of the angular momentum L in a gauge invariant point of view, provided that the hole is in the center. Different cases with the paramagnetic current, the diamagnetic current, and the coexistence of the above two,…
The influence of the geometry of a thin superconducting sample on the penetration of the magnetic field lines and the arrangement of vortices are investigated theoretically. We compare superconducting disks, squares and triangles with the same surface area having nonzero thickness. The coupled nonlinear Ginzburg-Landau equations are solved self-consistently and the important demagnetization effects are taken into account. We calculate and compare quantities like the free energy, the magnetization, the Cooper-pair density, the magnetic field distribution and the superconducting current density …
We analyze magnetic textures in a thin magnetic film and screening currents induced by these textures in a superconducting film. The films are supposed to be parallel and close to each other, but interact only via magnetic fields. We consider also vortices inside superconducting film and their interaction with magnetic textures. As examples of magnetic textures we consider magnetic dot and magnetic vortex. We derive the condition at which spontaneous formation of a vortex or a coupled vortex-magnetic defect is energetically favorable. It is proven that the normal component of magnetic field ge…
The set of the nonlinear Ginzburg-Landau equations is solved for an Al mesoscopic superconducting triangle of finite thickness. We calculate the distributions of the superconducting phase in the triangle and of the magnetic field in and near the triangle. The distribution of the superconducting phase in the triangle is studied as a function of the applied magnetic field. Possible scenarios of penetration of the magnetic field into the triangle are analyzed. We consider two different states: a single vortex state and a state in the form of a symmetric combination of three vortices and an antivo…
Harnessing the properties of vortices in superconductors is crucial for fundamental science and technological applications; thus, it has been an ongoing goal to locally probe and control vortices. Here, we use a scanning probe technique that enables studies of vortex dynamics in superconducting systems by leveraging the resonant behavior of a raster-scanned, magnetic-tipped cantilever. This experimental setup allows us to image and control vortices, as well as extract key energy scales of the vortex interactions. Applying this technique to lattices of superconductor island arrays on a metal, w…
A simple variational model is proposed to analyze the superconducting state in long cylindrical type-II superconductor placed in the external magnetic field. In the framework of this model, it is possible to solve the Ginzburg-Landau equations for the states with axially symmetric distributions of the order parameter. Phase transitions between different superconducting states are studied in the presence of external magnetic field and an equilibrium phase diagram of thin cylinder is obtained. The lower critical field of the cylindrical type-II superconductor with arbitrary values of radius and …
Vortex structures in mesoscopic cylinder placed in external magnetic field are studied under the general de Gennes boundary condition for the order parameter corresponding to the suppression of surface superconductivity. The Ginzburg-Landau equations are solved based on trial functions for the order parameter for vortex-free, single-vortex, multivortex, and giant vortex phases. The equilibrium vortex diagrams in the plane of external field and cylinder radius and magnetization curves are calculated at different values of de Gennes "extrapolation length" characterizing the boundary condition fo…
Direct observation of vortex states confined in mesoscopic regular triangle dots of amorphous MoGe thin films was made with a scanning superconducting quantum interference device microscope. The observed magnetic images illustrate clearly how vortices are distributed over the triangle dots by forming not only commensurate triangular clusters, but also unique patterns imposed by incommensurability. We discuss the results in terms of vortex shells and construct the packing sequence of vortices in the multiple shell structure.
The effects of the coupling between two electronic condensates in two-gap mesoscopic superconductors are studied within the Ginzburg-Landau theory using a finite difference technique. In applied magnetic field, we derive the dependency of the size of the vortex on the sample size and the strength of the Josephson coupling. In addition, we elaborate on the dependence of the critical temperature and field on the parameters of the coupled condensates. We demonstrate further the existence and stability of fractional states, for which the two condensates comprise different vorticity. Moreover, we a…
The electric charge density in mesoscopic superconductors with circular symmetry, i.e. disks and cylinders, is studied within the phenomenological Ginzburg-Landau approach. We found that even in the Meissner state there is a charge redistribution in the sample which makes the sample edge become negatively charged. In the vortex state there is a competition between this Meissner charge and the vortex charge which may change the polarity of the charge at the sample edge with increasing magnetic field. It is shown analytically that in spite of the charge redistribution the mesoscopic sample as a …
We discuss the magnetic response of gold-niobium proximity cylinders in the temperature range 100 μK<T<9 K. The temperature dependence of the susceptibility in the diamagnetic regime is described well by the quasiclassical Eilenberger theory including an elastic mean-free path l. In the mesoscopic regime, the temperature dependence of the reentrant paramagnetic susceptibility χ_para(T) \propto \exp[-L/3ξ^d_N(T)] is governed by the dirty limit coherence length ξ^d_N(T)=\sqrt{1/3ξ_N l_N}, with ξ_N the clean limit coherence length obtained from breakdown field measurements and l_N the measured me…
Phase transitions between different (i.e. giant and multi-vortex) superconducting states and between the superconducting-normal state of mesoscopic disks and rings are studied in the presence of an external magnetic field by solving the two non-linear Ginzburg-Landau equations self-consistently. The flux through a circular disk with a hole in the middle is not quantized.
Using the non-linear Ginzburg-Landau (GL) theory, we study the magnetic response of different shaped samples in the field-cooled regime (FC). For high external magnetic fluxes, the conventional diamagnetic response under cooling down can be followed by the paramagnetic Meissner effect (PME). A second-order transition from a giant vortex state to a multi-vortex state, with the same vorticity, occurs at the second critical field which leads to the suppression of PME.
We report on the direct observation of vortex states confined in equilateral and isosceles triangular dots of weak pinning amorphous superconducting thin films with a scanning superconducting quantum interference device microscope. The observed images illustrate not only pieces of a triangular vortex lattice as commensurate vortex states, but also incommensurate vortex states including metastable ones. We comparatively analyze vortex configurations found in different sample geometries and discuss the symmetry and stability of commensurate and incommensurate vortex configurations against deform…
Within the framework of the generalized time-dependent Ginzburg-Landau equations, we studied the influence of the magnetic self-field induced by the currents inside a superconducting sample driven by an applied transport current. The numerical simulations of the resistive state of the system show that neither material inhomogeneity nor a normal contact smaller than the sample width are required to produce an inhomogeneous current distribution inside the sample, which leads to the emergence of a kinematic vortex-antivortex pair (vortex street) solution. Further, we discuss the behaviors of the …
A projected order parameter is used to calculate, not only local minima of the Ginzburg-Landau energy functional, but also saddle points or energy barriers responsible for the metastabilities observed in superconducting mesoscopic disks (Geim et al. Nature {\bf 396}, 144 (1998)). We calculate the local minima magnetization and find the energetic instability points between vortex configurations with different vorticity. We also find that, for any vorticity, the supercurrent can reverse its flow direction on decreasing the magnetic field before one vortex can escape.
