Nucleation Of Superconductivity Research Articles

Domain-wall superconductivity in hybrid superconductor-ferromagnet structures

On the basis of a phenomenological Ginzburg-Landau approach we investigate the problem of order parameter nucleation in hybrid superconductor-ferromagnet systems with a domain structure in an applied external magnetic field. Both isolated domain boundaries and periodic domain structures in ferromagnetic layers are considered. We study the interplay between superconductivity localized at the domain walls and far from the walls and show that such an interplay determines a peculiar field dependence of the critical temperature ${T}_{c}.$ For a periodic domain structure the behavior of the upper critical field of superconductivity nucleation near ${T}_{c}$ is strongly influenced by the overlapping of the superconducting nuclei localized over different domains.

Surface superconducting states and paramagnetism in mesoscopic superconductors

In the framework of the Ginzburg-Landau equation, the temperature dependence of the upper critical field of small thin ringlike superconductors is studied. At equilibrium small parts of the phase diagram show paramagnetism for small hole sizes (larger than 15%). Their number and extension increase with the size of the hole. In these regions, only the inner part of the ring shows a positive magnetic moment. The order parameter density profile appears to change when crossing a first order transition line which separates different angular momentum values. We clarify the relationship between the localization of superconductivity nucleation and paramagnetism of these samples.

Nucleation of superconductivity in an Al mesoscopic disk with magnetic dot

We have studied the nucleation of superconductivity in a mesoscopic Al disk with a Co/Pd magnetic dot placed on the top by measuring the normal/superconducting phase boundary Tc(B). The measurements have revealed a pronounced asymmetry in the phase boundary with respect to the direction of the applied magnetic field, indicating an enhancement of the critical field when an applied magnetic field is oriented parallel to the magnetization of the magnetic dot. The theoretical Tc(B) curve is in a good agreement with the experimental data.

Nucleation of superconductivity in mesoscopic star-shaped superconductors

We study the phase transition of a star-shaped superconductor, which covers smoothly the range from zero to two dimensions with respect to the superconducting coherence length. Detailed measurements and numerical calculations show that the nucleation of superconductivity in this device is very inhomogeneous, resulting in rich structure in the superconducting transition as a function of temperature and magnetic field. The superconducting order parameter is strongly enhanced and mostly robust in regions close to multiple boundaries.

Vortex?antivortex patterns in mesoscopic superconductors

We have studied the nucleation of superconductivity in mesoscopic structures of different shape (triangle,square and rectangle). This was made possible by using an analytical gauge transformation for the vector potential A which gives An ¼ 0 for the normal component along the boundary line of the rectangle. As a consequence the superconductor– vacuum boundary condition reduces to the Neumann boundary condition. By solving the linearized Ginzburg–Landau equation with this boundary condition we have determined the field-temperature superconducting phase boundary and the corresponding vortex patterns. The comparison of these patterns for different structures demonstrates that the critical parameters of a superconductor can be manipulated and fine-tuned through nanostructuring. r 2003 Elsevier Science B.V. All rights reserved.

Domain wall superconductivity in ferromagnetic superconductors

On the basis of a phenomenological Ginzburg-Landau approach we investigate the problem of triplet order parameter nucleation in a ferromagnetic superconductor with a domain structure in an applied external magnetic field. The critical temperature of the superconductivity nucleation is shown to increase near the domain boundaries and to have a peculiar field dependence. Our results are also applied to a description of the superconductivity localized near the domain wall in $S/F$ heterostructures.

Superconducting Films in Perpendicular Fields and the Effect of the de Gennes Parameter

In this paper we study superconductivity of a thin film placed in a perpendicular magnetic field. We discuss the dependence of the upper critical field HC3 on the thickness l of the film and the Ginzburg--Landau parameter $\kappa$, and we examine nucleation of superconductivity. We show that a critical change occurs at $l=2\gamma\kappa^{-2}$. If $l>a\kappa^{-2}$ ($a>2\gamma$), the film exhibits type II behaviors: as the applied magnetic field decreases from $H_{C_3}$, superconductivity nucleates in a strip at the lateral surface and develops a lateral surface superconducting state. If $l\leq 2\g\kappa^{-2}+C\kappa^{-4}$, the film exhibits type I behaviors.

Upper critical field and location of surface nucleation of superconductivity

In this paper we improve the estimate obtained by Lu–Pan on the value of the upper critical field HC3(κ) for a cylindrical superconductor with cross section Ω being an arbitrary 2-dimensional smooth bounded domain. We also show that, when a homogeneous magnetic field is applied along the axis of the cylinder with magnitude of the field close to HC3, superconductivity nucleates first at the surface of the sample where the curvature of ∂Ω is maximal.

Fluctuation conductivity in superconducting MgB2

According to the crystal structure of MgB2 and band structure calculations, quasi-two-dimensional (2D) boron planes are responsible for the superconductivity. We report on critical-field and resistance measurements of 5.6-μm-thick MgB2 films grown on a sapphire single-crystal substrate. Resistivity measurements yield a temperature dependence of the fluctuation conductivity above the critical temperature, which agrees with the Aslamazov-Larkin and Maki-Thompson theory of fluctuations in layered superconductors, indicating a quasi-two-dimensional nucleation of superconductivity in MgB2.

Upper critical field for superconductors with edges and corners

The effect of non-smoothness of sample surfaces on the value of the upper critical field \(H_{C_3}\) and on the location of superconductivity nucleation is discussed. It is shown that, superconducting samples with edges and corners have higher value of \(H_{C_3}\) comparing to samples with smooth surfaces. Superconductivity nucleates first at the top and bottom edges in a cylinder with a finite height, and nucleates first at vertices in a cuboid.

On a Problem Related to Vortex Nucleation of Superconductivity

In this paper we study a singularly perturbed nonlinear partial differential system which arises in the mathematical theory of superheating field of superconductivity. We prove that the maximum points of the magnitude of solutions are located near the minimum point of curvature of domain boundary. This verifies rigorously a result of Chapman obtained by formal analysis regarding the location of the vortex nucleation. We also show that the solutions exhibit boundary layers.

Schrödinger operators with non-degenerately vanishing magnetic fields in bounded domains

We establish an asymptotic estimate of the lowest eigenvalue μ ( b F ) \mu (b\mathbf {F}) of the Schrödinger operator − ∇ b F 2 -\nabla _{b\mathbf {F}}^{2} with a magnetic field in a bounded 2 2 -dimensional domain, where curl F \mathbf {F} vanishes non-degenerately, and b b is a large parameter. Our study is based on an analysis on an eigenvalue variation problem for the Sturm-Liouville problem. Using the estimate, we determine the value of the upper critical field for superconductors subject to non-homogeneous applied magnetic fields, and localize the nucleation of superconductivity.

Nucleation of superconductivity in finite anisotropic superconductors and the evolution of surface superconductivity toward the bulk mixed state

In anisotropic superconductors having an arbitrary orientation of the sample surface relative to the crystal principal axes, the surface critical field H c 3 is less than 1.695H c 2 unless the field is situated along one of the principal crystal planes. Below H c 3 in the vicinity of nucleation, the order parameter scales as √H c 3 - H. Computational studies for infinite cylinders having rectangular cross sections are presented which show that, due to corners and a finite cross section, the surface superconductivity state persists for fields above the theoretically predicted value for semi-infinite samples. They also show that vortices exist within the surface superconductivity sheath above the bulk critical field.

Nucleation of superconductivity in a mesoscopic triangle

The nucleation of superconductivity in a mesoscopic equilateral triangle is studied experimentally by transport measurements and theoretically by using the linearized Ginzburg–Landau equation. The voltage and current leads, intrinsic to transport measurements, give rise to a broadening of the resistive transition R( T). However, by choosing the right resistance criterion to determine the experimental superconducting/normal phase boundary T c( H) and by reducing the coupling between the triangle and the contacts, achieved by changing the shape of the contacts, this influence can be minimized. From the theoretical study, we found that the trigonal symmetry of the sample has a profound effect on the superconducting state in the presence of a magnetic field H leading, in particular, to the formation of antivortices in symmetry-consistent states. A good agreement between the theory and the experimental T c( H) data is observed.

Nucleation of superconductivity in regular polygons: superconducting vector potential gauge approach

An approach to the Ginzburg–Landau problem for superconducting regular polygons is developed making use of an analytical gauge transformation for the vector potential A which gives A n =0 for the normal component along the boundary line of an arbitrary regular polygon. As a result the corresponding linearised Ginzburg–Landau equation reduces to an eigenvalue problem in the basis set of functions obeying Neumann boundary condition. The proposed approach allows for accurate calculations of the order parameter distributions at low calculational cost (small basis sets) for moderate applied magnetic fields. This is illustrated by considering the nucleation of superconductivity in squares and equilateral triangles where novel vortex patterns containing and antivortex in the centre are obtained on the T c– H phase boundary. The stability of these solutions against small deviations from the phase boundary line deeper into the superconducting state is investigated and the conditions for the experimental observation of the novel vortex patterns are discussed.

Vortex entry and nucleation of antivortices in a mesoscopic superconducting triangle.

The nucleation of superconductivity in mesoscopic equilateral triangles is investigated by using the linearized Ginzburg-Landau equation (LGLE). The trigonal symmetry of the sample has a profound effect on the superconducting state in the presence of a magnetic field H leading, in particular, to the formation of antivortices in symmetry-consistent states. For the same given irreducible representation, vortices enter always by three via the middle of the edges, approach the center, and then are dispatched towards the corners of the triangle. The measured superconducting phase boundary T(c)(H) is in good agreement with the T(c)(H) line found from the LGLE.

Ginzburg–Landau system and surface nucleation of superconductivity

Ginzburg–Landau system and surface nucleation of superconductivity

Surface Nucleation of Superconductivity in 3-Dimensions

In this paper we study the surface nucleation of superconductivity and estimate the value of the upper critical field HC3 for superconductors occupying arbitrary bounded smooth domains in R3. We show that HC3≃κ/β0, the ratio of the Ginzburg–Landau parameter κ and the first eigenvalue β0 of the Schrödinger operator with unit magnetic field on the half plane. When the applied magnetic field is spacially homogeneous and close to HC3, a superconducting layer nucleates on a portion of the surface at which the applied field is tangential to the surface. Nucleation under non-homogeneous applied fields is also discussed.

Nucleation of superconductivity in an overcooled normal domain

Relaxation of the overcooled normal domain with magnetic flux in type-I and type-II superconductors is considered. Two regimes of dynamics, depending on the domain size and the amount of trapped magnetic flux have been found: decay into single vortices and explosive nucleation of the topological vortices and antivortices. Small overcooled normal spots in type-II superconductors decay into a cluster of Abrikosov vortices while the restoration of superconductivity in large domains with weak magnetic fields leads to the creation of a long-living vortex-antivortex mixed state. In the presence of pinning centers in the sample this state can be frozen and persist indefinitely. Application of a week external magnetic field extracts antivortices from the sample thus causing net increase of the magnetic penetrating into the sample.

Nucleation of superconductivity in a mesoscopic loop of finite width

The normal/superconducting phase boundary T c has been calculated for mesoscopic loops as a function of an applied perpendicular magnetic field H. While for thin-wire loops and filled disks, the T c( H) curves are well known, the intermediate case, namely, mesoscopic loops of finite wire width, have been studied much less. The linearized first Ginzburg–Landau (GL) equation is solved with the proper normal/vacuum boundary conditions both at the internal and at the external loops radii. For thin-wire loops, the T c( H) oscillations are perfectly periodic, and the T c( H) background is parabolic (this is the usual Little–Parks effect). For loops of thicker wire width, there is a crossover magnetic field above which T c( H) becomes quasi-linear, with the period identical to the T c( H) of a filled disk (i.e., pseudoperiodic oscillations). This dimensional transition is similar to the 2D–3D transition for thin films in a parallel field, where vortices start penetrating the material as soon as the film thickness exceeds the temperature-dependent coherence length by a factor 1.8. For the presently studied loops, the crossover point is controlled by a similar condition. In the high-field ‘3D’ regime, a giant vortex state establishes, where only a surface superconducting sheath near the sample's outer radius is present.