Interaction of Josephson and Abrikosov vortices in a Y-Ba-Cu-O superconductor

The penetration of weak magnetic fields (0-n × 10⁻² T) into a Y-Ba-Cu-O ceramic supercon-ductor is studied. The nucleation fields for Abrikosov and Josephson vortices (fluxons) and the boundaries of the range in which the amplitude of the high-temperature superconductor response depends on the superposition of the dc field and weak variable fields caused by the fluxon mobility are experimentally determined.     

Electrodynamics of Abrikosov vortices: the field theoretical formulation

Electrodynamic phenomena related to vortices in superconductors have been studied since their prediction by Abrikosov, and seem to hold no fundamental mysteries. However, most of the effects are treated separately, with no guiding principles.We demonstrate that the relativistic vortex worldsheet in spacetime is the object that naturally conveys all electric and magnetic information, for which we obtain simple and concise equations. Breaking Lorentz invariance leads to down-to-earth Abrikosov vortices, and special limits of these equations include for instance dynamic Meissner screening and the AC Josephson relation. On a deeper level, we explore the electrodynamics of two-form sources in the absence of electric monopoles, in which the electromagnetic field strength itself acquires the characteristics of a gauge field. This novel framework leaves room for unexpected surprises.     

Is the Abrikosov model applicable for describing electronic vortices in plasmas?

A new model of electronic vortices in plasma is studied. The model assumes that the profile of the Lagrangian invariant I, equal to the ratio I=Ω/n of the electronic vorticity to the electron density, is given. The proposed approach takes into account the magnetic Debye scale r _B ≃B/4πen, which leads to breakdown of plasma quasineutrality. It is shown that the Abrikosov singular model cannot be used to describe electron vortices in plasmas because of the fundamental limitation on the electron vorticity on the axis of a vortex in a plasma. Analysis of the equations shows that in the model considered for the electronic vorticity, the total magnetic flux decreases when the size r ₀ of the region in which I≠0 becomes less than c/ω_pe (ω_pe is the electron plasma frequency). For ω _pe r ₀/c≪1, an electronic vortex is formed in which the magnetic flux decreases as r ₀ ² and the inertial component predominates in the electronic vorticity. The structure arising as ω _pe r ₀/c⇒0 is a narrow “hole” in the electron density, which can be identified from the spectrum of electromagnetic waves in this region. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 461–466 (10 April 1998)     

Magnetic flux trapping and broken Abrikosov vortices in yttrium HTSC ceramic samples

Direct evidence of the existence of broken Abrikosov vortices is obtained from measurements of the distribution and values of residual magnetic fields in ceramic yttrium HTSC samples after the switching off of a transport current. In this case, the intergrain magnetic induction averaged over the sample volume has the same direction as the field that was in the sample before the current was switched off.     

Inverse crystallization of a system of Abrikosov vortices with periodic pinning

A system of vortices in a quasi-two-dimensional HTSC plate with periodic pinning is considered. The magnetization curves are calculated by the Monte Carlo method for different values of an external magnetic field and different temperatures. It is shown that the vortex system with periodic pinning may crystallize with an increase in temperature.     

Ordered states and structural transitions in a system of Abrikosov vortices with periodic pinning

A system of Abrikosov vortices in a quasi-two-dimensional HTSC plate is considered for various periodic lattices of pinning centers. The magnetization and equilibrium configurations of the vortex density for various values of external magnetic field and temperature are calculated using the Monte Carlo method. It is found that the interaction of the vortex system with the periodic lattice of pinning centers leads to the formation of various ordered vortex states through which the vortex system passes upon an increase or a decrease in the magnetic field. It is shown that ordered vortex states, as well as magnetic field screening processes, are responsible for the emergence of clearly manifested peaks on the magnetization curves. Extended pinning centers and the effect of multiple trapping of vortices on the behavior of magnetization are considered. Melting and crystallization of the vortex system under the periodic pinning conditions are investigated. It is found that the vortex system can crystallize upon heating in the case of periodic pinning.     

A variational problem for a system of magnetic monopoles joined by Abrikosov vortices

An action functional, related to the Higgs model to field theory, depending on a complex scalar field and aU(1) connection is defined. The complex scalar field is a section of a line bundle associated to a principalU(1)-bundle with base space ³\{x ₁,...,x _n }. The pointsx ₁,...,x _n are the positions ofn magnetic monopoles of magnetic chargesm ₁,...,m _n, with . The existence of minimizers of the action functional is proven using direct methods of the calculus of variation. Regularity and decay properties of the minimizers are obtained. By constructing explicit comparison field configurations, we establish accurate upper and lower bounds for the action of the minimizers in a variety of special situations, e.g.n=2 andm ₁=–m ₂.     

Instability of Abrikosov vortices in a type-II superconductor-ferrite structure with a longitudinal electric field

The influence of the interaction of the Abrikosov vortices with the magnetization on the longitudinal vortex instability in a layered type-II superconductor-ferrite structure is analyzed. It is shown that in the vicinity of the orientational phase transition in the magnet, where the transverse susceptibility of the magnet is high, the longitudinal critical current in the structure can be almost 1.5 times smaller than the corresponding value in the isolated superconductor. Because of the influence of the nonlocality of the interaction between the vortices, such an effect can be observed only in structures with superconductors that have weak or moderate pinning. A structure is considered in which the thickness of the superconductor is significantly greater than the London magnetic-field penetration depth and the wavelength of the critical mode. Zh. Tekh. Fiz. 67, 28–34 (July 1997)     

Influence of the pinning of Abrikosov vortices on the propagation of surface magnetostatic waves in a ferromagnet-superconductor structure

The influence of surface-layer vortex pinning in a type-II superconductor on the propagation of surface magnetostatic waves in a ferromagnet-superconductor structure is analyzed. The pinning is assumed to be strong enough to prevent vortex displacement under the influence of the Lorentz force generated by the surface magnetostatic waves, so that the ground state of the superconductor is determined by the elastic properties of the vortex lattice and by pinning. In the given model the problem reduces to the analysis of the wave spectrum in the scattered field created by the disordered vortex surface layer. A calculation shows that the influence of this field on the surface magnetostatic-wave spectrum is slight and, hence, degradation of the shielding properties of the superconductor does not take place in the presence of strong vortex pinning (as opposed to the ferromagnet-ideal superconductor structure). Fiz. Tverd. Tela (St. Petersburg) 40, 32–35 (January 1998)     

Density of states in SF bilayers with arbitrary strength of magnetic scattering

We developed a self-consistent method for the calculation of the density of states N(ε) in SF bilayers. It is based on the quasi-classical Usadel equations and takes into account the suppression of superconductivity in the S layer due to the proximity effect of the F metal, as well as existing mechanisms of the spin dependent electron scattering. We demonstrate that the increase of the spin orbit or spin flip electron scattering rates results in completely different transformations of N(ε) at the free F layer interface. The developed formalism has been applied for the interpretation of the available experimental data. The text was submitted by the authors in English.     

Abrikosov Lattices in Finite Domains

In 1957 Abrikosov published his work on periodic solutions to the linearized Ginzburg-Landau equations. Abrikosov's analysis assumes periodic boundary conditions, which are very different from the natural boundary conditions the minimizer of the Ginzburg-Landau energy functional should satisfy. In the present work we prove that the global minimizer of the fully non-linear functional can be approximated, in every rectangular subset of the domain, by one of the periodic solution to the linearized Ginzburg-Landau equations in the plane. Furthermore, we prove that the energy of this solution is close to the minimum of the energy over all Abrikosov's solutions in that rectangle.     

Shape of a magnetic resonance line in a thin film on the surface of anisotropic superconductor with irregularly distributed Abrikosov’s vortices

The form of an electron paramagnetic resonance (EPR) in a thin paramagnetic film (λ/10, λ-London’s depth of magnetic field penetration into superconductor) overlying the surface of an anisotropic superconductor is calculated taking into account the local magnetic field non-uniformity of an irregular Abrikosov’s vortex lattice. It is shown that the form of EPR is noticeably varied with the degree of irregularity of the superconductor vortex lattice. It is suggested that an inclusion of this circumstance into consideration may essentially change the conclusions made on the lattice type and parameters of this superconductor, which are typically derived from the analysis of the EPR form. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 49–52, January, 2007.     

Modelling of Abrikosov Vortices in Three-Dimensional Nanostructures

Russian Physics Journal - COMSOL was used for the modelling of Abrikosov vortices in three-dimensional micro- and nano-sized structures. When modelling, boundary conditions were introduced into the...     

Abrikosov vortex core structure in a proximity-effect multilayer

The core structure of the Abrikosov vortex perpendicular to the layers of a proximity effect SN multilayer is discussed. We assume that the superconducting correlations are induced in N via the proximity effect and the dirty limit conditions are fulfilled. The approach for calculation of the local densities of states in N and S layers is developed in the framework of the quasiclassical Usadel equations. For the practically interesting case of SN bilayer, relevant to the STM spectroscopy, the densities of states and apparent STM vortex-core radius, related to the energy-dependent coherence length in N, are calculated.     

Inertial mass of the Abrikosov vortex

We show that a large contribution to the inertial mass of the Abrikosov vortex comes from transversal displacements of the crystal lattice. The corresponding part of the mass per unit length of the vortex line is M(l)=(m(2)(e)c(2)/64 pi alpha(2)mu lambda(4)(L))ln((lambda(L)/xi), where m(e) is the bare electron mass, c is the speed of light, alpha=e(2)/Planck's over 2 pi c approximately 1/137 is the fine structure constant, mu is the shear modulus of the solid, lambda(L) is the London penetration length, and xi is the coherence length. In conventional superconductors, this mass can be comparable to or even greater than the vortex core mass computed by Suhl [Phys. Rev. Lett. 14, 226 (1965)]].     

Velocity field vortices and Mermin-Ho vortices in two-component spinor BEC

In light of the φ-mapping topological current theory, two important vortex structures in two-component spinor BEC—the velocity field vortices and the Mermin-Ho vortices are discussed. It is revealed that these two different kinds of vortices are created respectively from the zero points of two different order parameter configurations in the condensates, and both their topological charges, locations and motions can be determined by the φ-mapping theory.