We predict that in a bulk type-1.5 superconductor the competing magnetic responses of the two components of the order parameter can result in a vortex interaction that generates group-stabilized giant vortices and unusual vortex rings in the absence of any extrinsic pinning or confinement mechanism. We also find within the Ginzburg-Landau theory a rich phase diagram with successions of behaviors like type-1 -> type-1.5 -> type-2 -> type-1.5 as temperature decreases.
The physics behind the rhombic$\to$square$\to$rhombic flux line lattice transformation in increasing fields is clarified on the basis of Eilenberger theory. We demonstrate that this reentrance observed in LuNi$_2$B$_2$C is due to intrinsic competition between superconducting gap and Fermi surface anisotropies. The calculations reproduce not only it but also predict yet not found lock-in transition to a square lattice with different orientation in higher field. In view of physical origin given, this sequence of transitions is rather generic to occur in four-fold symmetric superconductors.
The magnetic field dependence of the critical current is studied in single crystal samples of the weak pinning type-II superconductor 2H-NbSe$_2$ in the high temperature and the low field region of the (H,T) phase space, in the vicinity of the reentrant peak effect. The experimental results demonstrate various pinning regimes : a collective pinned quasi-ordered solid in the intermediate field that is destabilized in favor of disordered vortex phases in both high fields near H$_{c2}$ and at low fields near H$_{c1}$. The temperature evolution of the pinning behavior demonstrates how the amorphou…
We investigated the vortex phase diagram of needle shaped high quality NiBi3 single crystals by transport measurements. The current is applied along the crystalline b-axis of this intermetallic quasi-1D BCS superconductor. The single crystals show a Ginzburg-Levanchuk (Gi) parameter few orders of magnitude larger than other low Tc BCS superconductors. Vortex phase diagram, critical currents and pinning forces have been extracted from the experimental data. The main findings are: 1) Enhancement of the vortex liquid phase in comparison with low Tc superconductors, 2) reentrance of the liquid pha…
The peak effect (PE) has been observed in a twinned crystal of YBa$_2$Cu$_3$O$_{7-δ}$ for H$\parallel$c in the low field range, close to the zero field superconducting transition temperature (T$_c$(0)) . A sharp depinning transition succeeds the peak temperature T$_p$ of the PE. The PE phenomenon broadens and its internal structure smoothens out as the field is increased or decreased beyond the interval between 250 Oe and 1000 Oe. Moreover, the PE could not be observed above 10 kOe and below 20 Oe. The locus of the T$_p$(H) values shows a reentrant characteristic with a nose like feature locat…
We investigate the effects related to vortex core deformations when vortices approach each other. As a result of these vortex core deformations, the vortex-vortex interaction effectively acquires an attractive component leading to a variety of vortex patterns typical for systems with non-monotonic repulsive-attractive interaction, such as stripes, labyrinths, etc. The core deformations are anisotropic and can induce frustration in the vortex-vortex interaction. In turn, this frustration has an impact on the resulting vortex patterns, which are analyzed in the presence of additional random pinn…
We present the analysis of the structure of fermionic vortices with the spin-polarized core from a weak coupling limit to the unitary regime. We show the mechanism for the generation of the {\it reversed circulation} in the vortex core induced by an excess of majority spin particles. We introduce the classification of the polarized vortices based on the number of Fermi circles where the minigap vanishes. This provides a unique description of the vortex as one cannot smoothly map wave functions into one another corresponding to vortices differing by the number of Fermi circles. The effective ma…
Moving vortex matter, driven by transport currents independent of time, in which vortices and anti-vortices coexist is investigated theoretically in thin superconducting films with nanostructured defects. A simple London model is proposed for the vortex dynamics in films with periodic arrays of nanomagnets or cylindrical holes (antidots). Common to these films is that vortex anti-vortex pairs may be created in the vicinity of the defects by relatively small transport currents, because it adds to the current generated by the defects - the nanomagnets screening current, or the antidots backflow …
The reentrant nature of Peak Effect is established in a single crystal of 2H-NbSe_2 via electrical transport and dc magnetisation studies. The role of disorder on the reentrant branch of PE has been examined in three single crystals with varying levels of quenched random disorder. Increasing disorder presumably shrinks the (H,T) parameter space over which vortex array retains spatial order. Although, the upper branch of the PE curve is somewhat robust, the lower reentrant branch of the same curve is strongly affected by disorder.
Since it was first observed about 40 years ago [1], the peak effect has been the subject of numerous research mainly impelled by the desire to determine its exact mechanisms. Despite these efforts, a consensus on this question has yet to be reached. Experimentally, the peak effect indicates a transition from a depinned vortex phase to a reentrant pinning phase at high magnetic field. To study the effects of intrinsic pinning on the peak effect, we consider Fe$_{x}$Ni$_{1-x}$Zr$_{2}$ superconducting metallic glasses in which the vortex pinning force varies depending on the Fe content and in whi…
Scanning $μ$SQUID force microscopy is used to study magnetic flux structures in single crystals of the layered spin triplet superconductor Sr$\_{2}$RuO$\_{4}$. Images of the magnetic flux configuration above the $\vec{a}\vec{b}$-face of the cleaved crystal are acquired, mostly after field-cooling the sample. For low applied magnetic fields, individual vortices are observed, each carrying a single quantum of flux. Above 1 gauss, coalescence of vortices is discovered. The coalescing vortices may indicate the presence of domains of a chiral order parameter. When the applied field is tilted from t…
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 …
The properties of vortices in superconducting thin films are revisited. The interaction between two Pearl vortices in an infinite film is approximated at all distances by a simple expression. The interaction of a vortex with a regular lattice of real or image vortices is given. The two spring constants are calculated that one vortex in the vortex lattice feels when the surrounding vortices are rigidly pinned or are free. The modification of these London results by the finite size of real films is obtained. In finite films, the interaction force between two vortices is not a central force but d…
The interaction between a superconducting vortex or antivortex in a superconducting film and a magnetic dipole with in- or out-of-plane magnetization is investigated within the London approximation. The dependence of the interaction energy on the dipole-vortex distance and the film thickness is studied and analytical results are obtained in limiting cases. We show how the short range interaction with the magnetic dipole makes the co-existence of vortices and antivortices possible. Different configurations with vortices and antivortices are investigated.
The intervortex interaction is investigated in very anisotropic layered superconductors in tilted magnetic field. In such a case, the crossing lattice of Abrikosov vortices (AVs) and Josephson vortices (JVs) appears. The interaction between pancakes vortices (PVs), forming the AVs, and JVs produces the deformation of the AV line. It is demonstrated that in the result of this deformation a long range attraction between AVs is induced. This phenomenon is responsible for the dense vortex chains formation. The vortex structure in weak perpendicular magnetic field is the vortex chain phase, while i…
We discuss the zero field superconducting phase transition in a finite system of magnetically coupled superconducting layers. Transverse screening is modified by the presence of other layers resulting in topological excitations with fractional flux. Vortex stacks trapping a full flux and present at any finite temperature undergo an evaporation transition which corresponds to the depairing of fractional-flux vortices in individual layers. We propose an experiment with a bi-layer system allowing us to identify the dissociation of bound vortex molecules.
Vortex mass in Fermi superfluids and superconductors and its influence on quantum tunneling of vortices are discussed. The vortex mass is essentially enhanced due to the fermion zero modes in the core of the vortex: the bound states of the Bogoliubov qiasiparticles localized in the core. These bound states form the normal component which is nonzero even in the low temperature limit. In the collisionless regime $ω_0τ\gg 1$, the normal component trapped by the vortex is unbound from the normal component in the bulk superfluid/superconductors and adds to the inertial mass of the moving vortex. In…
We consider non-Abrikosov vortex solutions in liquid metallic hydrogen (LMH) in the framework of two-component Ginzburg-Landau model. We have shown that there are three types of non-Abrikosov vortices depending on chosen boundary conditions at the core of vortices, namely, Neumann (N)-type, Dirichlet (D)-type and Gross-Pitaevskii (GP)-type vortices. The Neumann-type vortex has a non-vanishing condensation at the core, that is different from the ordinary vortex, and the magnetic flux could be reversed as well in LMH. Furthermore, we have obtained a new type of a neutral vortex which has no magn…
We present theoretical and numerical investigations of vortices driven by strong dc and ac currents in long Josephson junctions described by a nonlinear integro-differential equation which takes into account nonlocal electrodynamics of films, vortex bremsstrahlung and Cherenkov radiation amplified by the attraction of vortices to the edges of the junction. The work focuses on the dynamics of vortices in Josephson junctions in thin films where the effects of Josephson nonlocality dominate but London screening is negligible. We obtained an exact solution for a vortex driven by an arbitrary time-…
We overview several recent experimental and numerical observations, which are at odds with the Vortex Glass theory of the freezing of disordered vortex matter. To reinvestigate the issue, we performed numerical simulations of the overdamped London - Langevin model, and use finite size scaling to analyze the data. Upon approaching the transition the initial Vortex Glass type criticality is arrested at some crossover temperature. Below this temperature the timescales continue growing very quickly, consistent with the Vogel-Fulcher form, while the spatial correlation length xi stops exhibiting an…
The profiles of local density of states (LDOS) around different vortex configurations in mesoscopic superconductors are studied taking account of the interference of quasiparticle waves experiencing Andreev reflection within the vortex cores and normal reflection at the boundaries or defects. For subgap energy levels these interference effects reveal themselves in a nontrivial dependence of the positions of the LDOS peaks on the intervortex distance and sample size: the peak positions generally do not coincide with the superconducting phase singularity points. The LDOS profiles are calculated …
We report muon spin rotation measurements on the conventional type-II superconductor V3Si that provide clear evidence for changes to the inner structure of a vortex due to the delocalization of bound quasiparticle core states. The experimental findings described here confirm a key prediction of recent microscopic theories describing interacting vortices. The effects of vortex-vortex interactions on the magnetic and electronic structure of the vortex state are of crucial importance to the interpretation of experiments on both conventional and exotic superconductors in an applied magnetic field.
Strains in superconductors due to moving vortices and vortex lattices are discussed. It is shown that the energy stored in elastic strains increases with vortex velocity. For moving vortex lattices, the elastic energy depends on velocity orientation relative to the lattice having minimum for the velocity directed along one of the unit cell vectors of the moving lattice. It is shown that for supersonic motion, the vortex induced stress field has a shape similar to supersonic shock waves.
We study theoretically and experimentally influence of pancake vortices on motion of the Josephson vortex lattice in layered high-temperature superconductors. Mobility of the Josephson vortices in layered superconductors is strongly suppressed by small amount of pancake-vortex stacks. Moving Josephson vortex lattice forces oscillating zigzag deformation of the pancake-vortex stacks contributing to damping. The salient feature of this contribution is its nonmonotonic dependence on the lattice velocity and the corresponding voltage. Maximum pancake effect is realized when the Josephson frequency…
We study the dynamics of vortices in an asymmetric ring channel driven by an external current I in a Corbino setup. The asymmetric potential can rectify the motion of vortices and cause a net flow without any unbiased external drive, which is called ratchet effect. With an applied ac current, the potential can rectify the motion of vortices in the channel and induce a dc net flow. We show that the net flow of vortices strongly depends on vortex density and frequency of the driving current. Depending on the density, we distinguish a "single-vortex" rectification regime (low density) determined …
The quantization of magnetic flux in superconductors is usually seen as vortices penetrating the sample. While vortices are unstable in bulk type I superconductors, restricting the superconductor causes a variety of vortex structures to appear. We present a systematic study of giant vortex states in type I superconductors obtained by numerically solving the Ginzburg-Landau equations. The size of the vortices is seen to increase with decreasing film thickness. In type I superconductors, giant vortices appear at intermediate thicknesses but they do not form a well-defined vortex lattice. In the …
Using numerical simulations we study the configurations, dynamics, and melting properties of vortex lattices interacting with elliptical pinning sites at integer matching fields with as many as 27 vortices per pin. Our pinning model is based on a recently produced experimental system [G. Karapetrov et al., Phys. Rev. Lett. 95, 167002 (2005)], and the vortex configurations we obtain match well with experimental vortex images from the same system. We find that the strong pinning sites capture more than one vortex each, and that the saturation number of vortices residing in a pin increases with a…
This paper has been withdrawn and replaced by a new version entitled "Vortex quantum dynamics of two dimensional lattice bosons" By Netanel H. Lindner, Assa Auerbach, Daniel P. Arovas, posted in arXiv:0810.2604. The calculations and results of the original manuscript were correct, and lead to several important conclusions about vortex dynamics and Hall conductance. However, we have dropped our conjecture, that vortices exhibit mutual Fermi statistics. The conjecture was based on the antisymmetry under exchange of two vortices, as revealed in the lowest eight many-body eigenstates of 16 sites t…
We have investigated vortex states in chiral helimagnet/superconductor bilayer systems under an applied external magnetic field Happl, using the Ginzburg-Landau equations. Effect of the chiral helimagnet on the superconductor is taken as a magnetic field HCHM, which is perpendicular to the superconductor and oscillates spatially. For Happl = 0 and weak HCHM, there appear pairs of up-and down-vortices. Increasing Happl, down-vortices gradually disappear, and number of up-vortices increases in the large magnetic field region. Then, up-vortices form parallel, triangular, or square structures.
We present a detailed study of the dynamic interactions between Josephson vortices and stacks of pancake vortices in a Bi2Sr2CaCu2O8 single crystal, obtained by measuring the effect of applied inplane magnetic field pulses on the c-axis magnetisation. The predominant interaction is to relax the system towards equilibrium. However, using a highly sensitive AC technique we are able to measure also the forces acting to drive the system away from equilibrium, consistent with the existence of dragging interactions between the Josephson and pancake systems. Such forces were discussed recently as the…
Interactions between vortices in planar superconducting films and a point magnetic dipole placed outside the film, and the creation of vortices by the dipole, are studied in the London limit. The exact solution of London equations for films of arbritrary thickness with a generic distribution of vortex lines, curved or straight, is obtained by generalizing the results reported by the author and E.H. Brandt (Phys. Rev. B {\bf 61}, 6370 (2000)) for films without the dipole. From this solution the total energy of the vortex-dipole system is obtained as a functional of the vortex distribution. The …
We demonstrate that, in contrast to the single-component Abrikosov vortex, in two-component superconductors vortex solutions with exponentially screened magnetic field exist only in exceptional cases: in the case of vortices carrying an integer number of flux quanta, and in a special parameter limit for half-quantum vortices. For all other parameters the vortex solutions have delocalized magnetic field with a slowly decaying tail. Furthermore, we demonstrate a new effect which is generic in two-component systems but has no counterpart in single-component systems: on exactly half of the paramet…
Superconductors often contain quantized microscopic whirlpools of electrons, called vortices, that can be modeled as one-dimensional elastic objects. Vortices are a diverse playground for condensed matter because of the interplay between thermal fluctuations, vortex-vortex interactions, and the interaction of the vortex core with the three-dimensional disorder landscape. While vortex matter has been studied extensively, the static and dynamic properties of an individual vortex have not. Here we employ magnetic force microscopy (MFM) to image and manipulate individual vortices in detwinned, sin…
The dynamics of magnetic vortices in the mixed state of d-wave superconductors is affected by interaction with quasiparticles near the gap nodes. We study this effect by computing the overlap of the ground state wave functions of the nodal quasiparticles in a two-dimensional d-wave superconductor as the ground state changes in response to the motion of the vortex. We find that the overlap is strongly suppressed. This orthogonality catastrophe is specific to a half-quantum vortex and disappears in the case of a doubly-quantized vortex. This implies strong inhibition of the motion of half-quantu…
Here we report a study of vortex states in a thin superconducting film with a magnetic dot grown upon it by means of a method based on London-Maxwell equations. Vortices with single quantum flux ($Φ_0 = h c / 2 e$), giant vortices (vortices with multiple flux) as well as antivortices (vortices with negative vorticity) are taken into consideration. It turns out that giant vortices occur, when the dot's size is sufficiently smaller ($R \leq 4.5 ξ$) than the effective penetration depth $Λ$. In the case of a dot with sufficiently large size ($R \geq 6 ξ$), the vortices with single quantum flux dom…
We use large-scale Monte-Carlo simulations to study thermal fluctuations in chiral $p$-wave superconductors in an applied magnetic field in three dimensions. We consider the thermal stability of previously predicted unusual double-quanta flux-line lattice ground states in such superconductors. In previous works it was shown that, neglecting thermal fluctuations, a chiral $p$-wave superconductor forms an hexagonal lattice of doubly-quantized vortices, except extremely close to the vicinity of $H_{c2}$ where double-quanta vortices split apart. We find dissociation of double-quanta vortices drive…
We present measurements of the fluctuation superconductivity in an underdoped thin film of La$_{1.905}$Sr$_{0.095}$CuO$_4$ using time-domain THz spectroscopy. We compare our results with measurements of diamagnetism in a similarly doped crystal of La$_{2-x}$Sr$_x$CuO$_4$. We show through a vortex-plasma model that if the fluctuation diamagnetism solely originates in vortices, then they must necessarily exhibit an anomalously large vortex diffusion constant, which is more than two orders of magnitude larger than the Bardeen-Stephen estimate. This points to either the extremely unusual propertie…
The magnetic field $h_z$ of a moving Pearl vortex in a superconducting thin-film in $(x,y)$ plane is studied with the help of time-dependent London equation. It is found that for a vortex at the origin moving in $+x$ direction, $h_z(x,y)$ is suppressed in front of the vortex, $x>0$, and enhanced behind ($x<0$). The distribution asymmetry is proportional to the velocity and to the conductivity of normal quasiparticles. The vortex self-energy and the interaction of two moving vortices are evaluated.
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 $a_0$, antidot diameter $d$, lattice symmetry, orientation, etc) 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 tw…
In strongly anisotropic layered superconductors in tilted magnetic fields the Josephson vortex lattice coexists with the lattice of pancake vortices. Due to the interaction between them, the dissipation of the Josephson-vortex lattice occurs to be very sensitive to the presence of the pancake vortices. If the c-axis magnetic field is smaller then the corresponding lower critical field, the pancake stacks are not formed but the individual pancakes may exist in the fluctuational regime either near surface in large-size samples or in the central region for small-size mesas. We calculate the contr…
A microscopic, quantum mechanical model for neutron vortices in the crust of a neutron star is presented. After a brief introduction to the Bogoliubov- de Gennes equations, which form the basis for our calculations, we present results for density distributions, vortex core sizes and vortex energies, both for an isolated neutron vortex and for the case when the vortex core overlaps with a cylindrical nucleus. Earlier results on the vortex core size are confirmed, indicating a much less dramatic variation of the vortex core size with density than predicted by the BCS formula.
We consider interaction of vortices in the vector complex Ginzburg--Landau equation (CVGLE). In the limit of small field coupling, it is found analytically that the interaction between well-separated defects in two different fields is long-range, in contrast to interaction between defects in the same field which falls off exponentially. In a certain region of parameters of CVGLE, we find stable rotating bound states of two defects -- a ``vortex molecule".
The magnetic flux noise induced by vortices in thin superconducting films is studied. Rigid vortices in thin films as well as pancake vortices in the pancake gas regime are addressed. The vortex dynamics is described by a Feynman path integral which fully accounts for the balance between vortex entropy and vortex energetics. We find that vortex pair creation (annihilation) in the presence of pinning is a natural source for noise with a 1/f spectrum.
The local effect of the Josephson vortices on the vortex lattice melting process in \BSCCO crystals in the presence of an in-plane field $H_{ab}$ is studied by differential magneto-optical imaging. The melting process is found to commence along the Josephson vortex stacks, forming a mesomorphic phase of periodic liquid and solid lamellas, the direction and spacing of which are controlled by $H_{ab}$. The reduction of the local melting field $H_m$ along the Josephson vortex stacks is more than an order of magnitude larger than the reduction of the average bulk $H_m$ by $H_{ab}$.
In this paper we describe a version of London Langevin molecular dynamics simulations that allows for investigations of the vortex lattice melting transition in the highly anisotropic high-temperature superconductor material Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. We include the full electromagnetic interaction as well as the Josephson interaction among pancake vortices. We also implement periodic boundary conditions in all directions, including the z-axis along which the magnetic field is applied. We show how to implement flux cutting and reconnection as an analog to permutations in the multilevel Mon…
The unzipping of vortex lines using magnetic-force microscopy from extended defects is studied theoretically. We study both the unzipping isolated vortex from common defects, such as columnar pins and twin-planes, and the unzipping of a vortex from a plane in the presence of other vortices. We show, using analytic and numerical methods, that the universal properties of the unzipping transition of a single vortex depend only on the dimensionality of the defect in the presence and absence of disorder. For the unzipping of a vortex from a plane populated with many vortices is shown to be very sen…
Multi-quanta, or giant, vortices (GVs) are known to appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for the formation of GVs. Using Bitter decoration to visualise vortices in small Nb disks, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters or even GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning.
We report a new nonlocal effect in vortex matter, where an electric current confined to a small region of a long and sufficiently narrow superconducting wire causes vortex flow at distances hundreds of inter-vortex separations away. The observed remote traffic of vortices is attributed to a very efficient transfer of a local strain through the one-dimensional vortex lattice, even in the presence of disorder. We also observe mesoscopic fluctuations in the nonlocal vortex flow, which arise due to "traffic jams" when vortex arrangements do not match a local geometry of a superconducting channel.
Superconducting materials with noncentrosymmetric lattices lacking space inversion symmetry exhibit a variety of interesting parity-breaking phenomena, including the magneto-electric effect, spin-polarized currents, helical states, and the unusual Josephson effect. We demonstrate, within a Ginzburg-Landau framework describing noncentrosymmetric superconductors with $O$ point group symmetry, that vortices can exhibit an inversion of the magnetic field at a certain distance from the vortex core. In stark contrast to conventional superconducting vortices, the magnetic-field reversal in the parity…
We propose a two-path vortex interferometry experiment based on the Aharonov-Casher effect for detecting the non-Abelian nature of vortices in a chiral p-wave superconductor. The effect is based on observing vortex interference patterns upon enclosing a finite charge of externally controllable magnitude within the interference path. We predict that when the interfering vortices enclose an odd number of identical vortices in their path, the interference pattern disappears only for non-Abelian vortices. When pairing involves two distinct spin species, we derive the mutual statistics between half…
In contrast to charge vortices in a superfluid, spin vortices in a ferromagnetic condensate move inertially (if the condensate has zero magnetization along an axis). The mass of spin vortices depends on the spin-dependent interactions, and can be measured as a part of experiments on how spin vortices orbit one another. For Rb87 in a 1 micron thick trap m_v is about 10^-21 kg.
We consider the vortex matter in a three-dimensional two-component superconductor with individually conserved condensates with different bare phase stiffnesses in a finite magnetic field, such as the projected superconducting state of liquid metallic hydrogen. The ground state is an Abrikosov lattice of {\it composite}, i.e. co-centered, vortices in both order parameters. We investigate quantitatively two novel phase transitions when temperature is increased at fixed magnetic field. {\it i)} A ``vortex sub-lattice melting" phase transition where vortices in the field with lowest phase stiffnes…
We study quantized vortices in ${}^{3}P_{2}$ superfluids using a microscopic theory for the first time. The theory is based on the Eilenberger equation to determine the order parameters and the Bogoliubov-de Gennes (BdG) equation to obtain the eigenenergies and the core magnetization. Within axisymmetric vortex configurations, we find several stable and metastable vortex configurations which depend on the strength of a magnetic field, similar to a $v$ vortex and $o$ vortex in $^3$He superfluids. We demonstrate that the $o$ vortex is the most stable axisymmetric vortex in the presence of a stro…
We study the Abrikosov-Nielsen-Olesen multi-vortices. Using a numerical code we are able to solve the vortex equations with winding number up to n=25,000. We can thus check the wall vortex conjecture previously made in hep-th/0507273 and hep-th/0507286. The numerical results show a remarkable agreement with the theoretical predictions.
