ID: cond-mat/9908451

Annular Vortex Solutions to the Landau-Ginzburg Equations in Mesoscopic Superconductors

August 30, 1999

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Dynamics and heat diffusion of Abrikosov's vortex-antivortex pairs during an annihilation process

August 15, 2017

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E C S Duarte, E Sardella, ... , Zadorosny R
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The manipulation and control of vortex states in superconducting systems are of great interest in view of possible applications, for which mesoscopic materials are good candidates. In this work, we studied the annihilation dynamics and the dissipative aspects of an Abrikosov's vortex-antivortex pair in a mesoscopic superconducting system with a concentric hole. The generalized time-dependent Ginzburg-Landau equations were numerically solved. The main result is the appearance ...

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Giant vortices in the Ginzburg-Landau description of superconductivity

December 21, 2001

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Vincent Hakim, Anaël Lemaître, Kirone Mallick
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Recent experiments on mesoscopic samples and theoretical considerations lead us to analyze multiply charged ($n>1$) vortex solutions of the Ginzburg-Landau equations for arbitrary values of the Landau-Ginzburg parameter $\kappa$. For $n\gg 1$, they have a simple structure and a free energy ${\cal F}\sim n$. In order to relate this behaviour to the classic Abrikosov result ${\cal F}\sim n^2$ when $\kappa\to +\infty$, we consider the limit where both $n\gg 1$ and $\kappa\gg1$...

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Magnetic Vortices, Abrikosov Lattices and Automorphic Functions

August 25, 2013

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Israel Michael Sigal
Mathematical Physics
Pattern Formation and Solito...

We address the macroscopic theory of superconductivity - the Ginzburg-Landau theory. This theory %Macroscopic theory of superconductivity is based on the celebrated Ginzburg - Landau equations. First developed to explain and predict properties of superconductors, these equations form an integral part - Abelean-Higgs component - of the standard model of particle physics and, in general, have a profound influence on physics well beyond their original designation area. %These ar...

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Abrikosov Lattice Solutions of the Ginzburg-Landau Equations

November 12, 2009

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T. Tzaneteas, I. M. Sigal
Mathematical Physics

Building on the earlier work of Odeh, Barany, Golubitsky, Turski and Lasher we give a proof of existence of Abrikosov vortex lattices in the Ginzburg-Landau model of superconductivity.

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Zero magnetic-field orbital vortices in s-wave spin-singlet superconductors

May 19, 2021

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Maria Teresa Mercaldo, Carmine Ortix, ... , Cuoco Mario
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Mesoscale and Nanoscale Phys...

Breaking of time-reversal and point-group spatial symmetries can have a profound impact on superconductivity. One of the most extraordinary effects, due to the application of a magnetic field, is represented by the Abrikosov vortices with charged supercurrents circulating around their cores. Whether a similar phenomenon can be obtained by exploiting spatial symmetry breaking, e.g. through electric fields or mechanical strain, is a fundamentally relevant but not yet fully sett...

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Nucleation and Arrangement of Abrikosov Vortices in Hybrid Superconductor-Ferromagnetic Nanostructure

November 19, 2024

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Sara Memarzadeh, Mateusz Gołębiewski, ... , Kłos Jarosław W.
Superconductivity
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This study investigates the nucleation, dynamics, and stationary configurations of Abrikosov vortices in hybrid superconductor-ferromagnetic nanostructures exposed to inhomogeneous magnetic fields generated by a ferromagnetic nanodot. Using time-dependent Ginzburg-Landau simulations and Maxwell's equations, we observe and provide an explanation for the evolution of curved vortex structures that undergo creep-like deformation while reaching a steady state. Spatial variations i...

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GINZBURG-LANDAU THEORY OF VORTICES IN $d$-WAVE SUPERCONDUCTORS

March 7, 1995

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A. J. Berlinsky, A. L. Fetter, M. Franz, ... , Soininen P. I.
Condensed Matter
Superconductivity

Ginzburg-Landau theory is used to study the properties of single vortices and of the Abrikosov vortex lattice in a $d_{x^2-y^2}$ superconductor. For a single vortex, the $s$-wave order parameter has the expected four-lobe structure in a ring around the core and falls off like $1/r^2$ at large distances. The topological structure of the $s$-wave order parameter consists of one counter-rotating unit vortex, centered at the core, surrounded by four symmetrically placed positive ...

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On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations

December 8, 2011

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T. Tzaneteas, I. M. Sigal
Mathematical Physics

Building on earlier work, we have given in our paper in Contemporary Mathematics 535, 195-213, 2011 (referred here as [TS]) a proof of existence of Abrikosov vortex lattices in the Ginzburg-Landau model of superconductivity and have shown that the triangular lattice gives the lowest energy per lattice cell. After [TS] was published, we realized that it proves a stronger result than was stated there. This result is recorded in the present paper. The proofs remain the same as i...

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Vortex Structure Around a Magnetic Dot in Planar Superconductors

October 23, 1995

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I. K. Marmorkos, A. Matulis, F. M. Peeters
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The problem of the giant vortex state around a magnetic dot which is embedded in a superconducting film is investigated. The full non-linear, self-consistent Ginzburg-Landau equations are solved numerically in order to calculate the free energy, the order parameter of the host superconductor, the internal magnetic field due to the supercurrents, the corresponding current density, the magnetization probed in the vicinity of the dot, and the normal electron density as a functio...

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Vortical versus skyrmionic states in mesoscopic \emph{p}-wave superconductors

September 16, 2015

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V. Fernández Becerra, E. Sardella, ... , Milošević M. V.
Superconductivity

We investigate the superconducting states that arise as a consequence of mesoscopic confinement and a multi-component order parameter in the Ginzburg-Landau model for $p\,$-wave superconductivity. Conventional vortices, but also half-quantum vortices and skyrmions are found as the applied magnetic field and the anisotropy parameters of the Fermi surface are varied. The solutions are well differentiated by a topological charge that for skyrmions is given by the Hopf invariant ...

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