Giant Vortex State Research Articles

Superconducting phase transitions in thin mesoscopic rings with enhanced surface superconductivity

The superconducting phase transitions between different vortex states with the magnetic field for a thin mesoscopic superconducting ring surrounded by a medium that enhanced its superconductivity near the boundary are investigated by the phenomenological Ginzburg-Landau theory. The transitions between different giant vortex states and between the giant vortex and multivortex states with $\ensuremath{\Delta}Lg1$ ($L$ is the vorticity of the vortex state) are found for a small ring with increasing surface enhancement. The influences of the surface enhancing superconducting effect and the inner radius as well as the temperature on phase transition are studied by examining the $H\text{\ensuremath{-}}\ensuremath{\mid}\ensuremath{\xi}∕b\ensuremath{\mid}$, $H\text{\ensuremath{-}}{R}_{i}$, and $H\text{\ensuremath{-}}T$ phase diagrams, respectively. Further increasing the effect of enhanced surface superconductivity, we find the reentrant transition with the same vorticity and the transitions between the stable multivortex states with $\ensuremath{\Delta}Lg1$ for different ring inner radii. We also investigate the vortex configurations for a relatively large ring, and the vortex state with two stable vortex shells can be found as the ground state due to the enhanced surface superconductivity.

Temperature-dependent vortex motion in a square mesoscopic superconducting cylinder: Ginzburg-Landau calculations

In this work we investigate the dynamics of vortices in a square mesoscopic superconductor. As time evolves we show how the vortices are nucleated into the sample to form a multivortex, single vortex, and giant vortex states. We illustrate how the vortices move around at the transition fields before they accommodate into an equilibrium configuration. We also calculate the magnetization and the free energy as functions of the applied magnetic field for several values of temperature. In addition, we evaluate the upper critical field.

Giant vortices in rotating electron droplets

We predict the formation of giant vortices in quasi-two-dimensional quantum dots at high magnetic fields, i.e., in rapidly rotating electron droplets. Our numerical results of quantum dots confined by a flat, anharmonic potential show ground states where vortices are accumulated in the center of the dot, thereby leading to large cores in the electron and current densities. The phenomenon is analogous to what was recently found in rotating Bose-Einstein condensates. The giant-vortex states leave measurable signatures in the ground-state energetics. The conditions for the giant-vortex formation as well as the internal structure of the vortex cores are discussed.

Two kinds of vortex states in thin mesoscopic superconductors

Experimentally, multivortex states and giant vortex states in mesoscopic superconductors can be distinguished directly by using the multiple-small-tunnel-junctions, and indirectly by studying the temperature dependence of the expulsion fields. These experimental results are compared with the theoretical prediction from the nonlinear Ginzburg- Landau theory.

Novel Commensurability Effects in Superconducting Films with Antidot Arrays

Vortex configurations in superconducting films with regular arrays of antidots (holes) are calculated within the nonlinear Ginzburg-Landau theory. In addition to the well-established matching phenomena, we predict (i) the nucleation of giant-vortex states between the antidots, (ii) the combination of giant- and multivortices at rational matching fields, and (iii) for particular values of the vorticity, symmetry imposed creation of vortex-antivortex configurations.

Size dependence of the vortex states in mesoscopic superconductors

We investigated the sample size dependence of the types of vortex states, i.e., multivortex states or giant vortex states, in mesoscopic superconducting squares by using the temperature dependence of vortex expulsion fields. The giant vortex states are stable in small samples and at high magnetic fields. The experimental results are compared with theoretical simulations based on the nonlinear Ginzburg–Landau theory.

Experimental study on giant vortex and multivortex states in mesoscopic superconductors

Two experimental methods for distinguishing between giant vortex and multivortex states in mesoscopic superconductors are described: the multiple-small-tunnel-junction method and the temperature dependence of vortex expulsion fields. The former provides a direct evidence for the existence of the giant vortex state in disks, while the latter might be applicable to mesoscopic superconductors with various shapes such as squares and triangles. The experimental results are well reproduced in numerical results based on the nonlinear Ginzburg–Landau theory.

Charge distribution in thin mesoscopic superconducting rings with enhanced surface superconductivity

The charge distribution in a thin mesoscopic superconducting ring with enhanced surface superconductivity (of a negative surface extrapolation length $b$) is investigated by the phenomenological Ginzburg-Landau theory. The nature of charge distribution is considerably influenced by the extrapolation length $b$, the inner and outer radius, and the applied magnetic field. We find a complete negative charge distribution besides the conventional charge distributions of charging vortex states in the Meissner state and the giant vortex state. In addition, one type of charge distribution that only exists in a giant vortex state can also be found in the Meissner state for a ring with a small inner radius. For the multivortex state, we find that the stable multivortex state can exist in small mesoscopic superconducting rings that we studied. The charge distributions for different kinds of multivortex states are given.

Dependence of the charge distribution on the size of thin mesoscopic rings

The influence of the size of thin mesoscopic superconducting ring on the charge distribution is investigated by the phenomenological Ginzburg–Landau theory. For a giant vortex state of angular quantum number L, we find that three physical quantities, that is, the critical radius R cr which corresponds to a maximum upper nucleation field H nuc , u for a disk sample, the critical outer radius R o , cr that gives a maximum value of the minimum inner radius R i , min beyond which the vortex state L can possibly be excited, and the critical inner radius R i , cr which leads to a maximum upper nucleation field H nuc , u in comparison with other inner radii for a fixed outer radius R o , determine the feature of boundaries of the phase diagram for charge distributions.

Multivortex and giant vortex states near the expulsion and penetration fields in thin mesoscopic superconducting squares

The temperature dependence of the vortex penetration and expulsion magnetic fields are investigated, both theoretically and experimentally, for mesoscopic superconducting squares. The small-tunnel-junction method is used to determine the transition fields between the different vortex states. We found that the penetration fields decrease with increasing temperature, while the expulsion fields for a particular vorticity may increase, decrease or be independent of temperature. Using the Ginzburg-Landau theory we link the different temperature dependencies to the configuration of the vortex state, i.e. giant vortex state versus multivortex state. The vortex state consisting of four vortices has a larger stability region which is most pronounced in a certain high-temperature range.

Vortex lattice in effective type-I superconducting films with periodic arrays of submicron holes

The vortex matter and related phenomena in superconducting films with periodic arrays of microholes (antidots) are studied within the nonlinear Ginzburg–Landau (GL) theory. By varying the GL parameter κ, the vortex–vortex interaction is fine tuned, from repulsive to attractive behavior. This interaction is of crucial importance for equilibrium vortex structures, the saturation number of the antidots, and the related quantities, such as critical current. Due to vortex attraction in effectively type-I samples, the giant-vortex state becomes energetically favorable (contrary to the type-II behavior). For the same reason, the number of vortices which can be captured by antidots, increases with decreasing κ. As a result, for given magnetic field, the critical current is larger for effectively type-I superconductors than in conventional type-II cases.

Transition to the giant vortex state in a harmonic-plus-quartic trap

We consider a rapidly rotating Bose-condensed gas in a harmonic-plus-quartic trap. At sufficiently high rotation rates, the condensate acquires an annular geometry with the superposition of a vortex lattice. With increasing rotation rate, the lattice evolves into a single ring of vortices. Of interest is the transition from this state to the giant vortex state in which the circulation is carried by only a central vortex. By analyzing the Gross-Pitaevskii energy functional variationally, we have been able to map out the phase boundary between these two states as a function of the rotation rate and the various trapped gas parameters. For strong interactions, the transition is first order. Our variational results are in good qualitative agreement with those obtained by means of a direct numerical solution of the Gross-Pitaevskii equation.

Dynamics of rapidly rotating Bose-Einstein condensates in a harmonic plus quartic trap

A two-dimensional rapidly rotating Bose-Einstein condensate in a harmonic plus quartic trap is expected to have unusual vortex states that do not occur in a pure harmonic trap. At a critical rotation speed ${\ensuremath{\Omega}}_{h}$, a central hole appears in the condensate, and at some faster rotation speed ${\ensuremath{\Omega}}_{g}$, the system undergoes a transition to a giant vortex state with pure irrotational flow. Using a time-dependent variational analysis, we study the behavior of an annular condensate with a single concentric ring of vortices. The transition to a giant vortex state is investigated by comparing the energy of the two equilibrium states (the ring of vortices and the giant vortex) and also by studying the dynamical stability of small excitation modes of the ring of vortices.

Giant and multivortex states in mesoscopic superconducting disks

Transitions between different multivortex states and transitions between multivortex states and giant vortex states are observed in mesoscopic superconducting disks using the multiple-small-tunnel-junction method. These results are compared to theoretical calculations within the framework of the nonlinear Ginzburg–Landau theory. We find a good qualitative agreement between the theoretical and experimental results, when we assume that a small defect is present near the center of the experimental sample.

Vortex Imaging in Microscopic Superconductors With a Scanning SQUID Microscope

Direct observation of vortex arrangement in microscopic superconductors is achieved with a scanning SQUID microscope. Newly 2 /spl mu/m diameter sensing pickup coil is developed for the observation of giant vortex state. Vortex arrangements in 10 /spl mu/m triangles is investigated with the new pickup device. No giant vortex state, however, can be seen under this experimental condition. Further investigation is needed.

Magnetically induced splitting of a giant vortex state in a mesoscopic superconducting disk

The nucleation of superconductivity in a superconducting disk with a $\mathrm{Co}∕\mathrm{Pt}$ magnetic triangle was studied. We demonstrate that when the applied magnetic field is parallel to the magnetization of the triangle, the giant vortex state of vorticity three splits into three individual ${\ensuremath{\Phi}}_{0}$ vortices, due to a pronounced influence of the ${\mathrm{C}}_{3}$ symmetry of the magnetic triangle. As a result of a strong pinning of the three vortices by the triangle, their configuration remains stable in a broad range of applied magnetic fields. For sufficiently high fields, ${\ensuremath{\Phi}}_{0}$ vortices merge and the nucleation occurs through the giant vortex state. The theoretical analysis of this reentrant behavior at the phase boundary, obtained within the Ginzburg-Landau formalism, is in excellent agreement with the experimental data.

Vortex-state-dependent phase boundary in mesoscopic superconducting disks

The temperature dependence of the vortex penetration and expulsion fields in mesoscopic superconducting disks are studied. We experimentally find that the penetration field decreases with increasing temperature for all values of the vorticity. On the other hand, the temperature dependence of the expulsion fields shows two regimes: For some vortex states the expulsion field increases with temperature, while for other states it is almost temperature independent. A numerical study based on the nonlinear Ginzburg-Landau theory confirms that the former regime corresponds to multivortex states and the latter to giant vortex states. The origin of this difference is discussed.

Charge distributions due to paramagnetism and diamagnetism in thin mesoscopic superconducting rings

The charge distribution in a thin mesoscopic superconducting ring is investigated by the phenomenological Ginzburg–Landau theory. Considering a ring in a giant vortex state, we find that the charge near the inner radius may change its sign from negative to positive with increasing the applied field. It is also found that the charge distributions are due to the competition between the paramagnetic Meissner effect and the diamagnetic Meissner effect.

Experimental Evidence for Giant Vortex States in a Mesoscopic Superconducting Disk

The 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 to make the first experimental distinction between the giant vortex states and multivortex states. Moreover, we experimentally find a magnetic-field induced rearrangement and combination of vortices. The experimental results are well reproduced in numerical results based on the nonlinear Ginzburg-Landau theory.

Superconducting vortex state in a mesoscopic disk containing a blind hole

Within the phenomenological nonlinear Ginzburg-Landau theory, we studied the superconducting state of a mesoscopic superconducting disk with a circular blind hole. The influence of the smoothness of the blind hole edge, the thickness and size of the blind hole on the superconducting condensate and the vortex state is examined. We found that the presence of the blind hole in the superconductor increases the superconducting/normal transition field. For large radii of the blind hole the maximal number of vortices that can nucleate in the sample increases with decreasing thickness of the blind hole. Vortices are preferentially captured in the blind hole and for a sufficiently large radius of the blind hole, the multivortex structure becomes energetically favorable. A gradual transition from a multivortex to a giant vortex state is observed.