Related papers: Abrikosov Vortex Lattices at Weak Magnetic Fields
We have found several families of vortex soliton solutions in two-dimensional discrete dissipative systems governed by the cubic-quintic complex Ginzburg-Landau equation. There are symmetric and asymmetric solutions, and some of them have…
The spatial distribution of fields and currents in confining theories can give direct evidence of dual superconductivity. We review the behavior of vortices in the lattice Higgs effective theory. We discuss the techniques for finding these…
We study analytically the $d$-wave holographic superconductors with Lifshitz scaling in the presence of external magnetic field. The vortex lattice solutions of the model have also been obtained with different Lifshitz scaling. Our results…
We elaborate a theory of giant vortices [1] based on an asymptotic expansion in inverse powers of their winding number $n$. The theory is applied to the analysis of vortex solutions in the abelian Higgs (Ginzburg-Landau) model. Specific…
The magnetic field distribution, the magnetic flux, and the free energy of an Abrikosov vortex loop near a flat surface of type--II superconductors are calculated in the London approximation. The shape of such a vortex line is a semicircle…
We prove the existence of non-constant time periodic vortex solutions to the Gross-Pitaevskii equations for small but \textit{fixed} $\varepsilon > 0.$ The vortices of these solutions follow periodic orbits to the point vortex system of…
In the main part of this PhD thesis, we consider a periodically realized microscopic superconductor described by BCS theory, which is subject to external electromagnetic fields. We show that the superconductor is properly described by…
A type-II superconductor survives in an external magnetic field by admitting an Abrikosov lattice of quantized vortices. This is an imprint of the Aharonov-Bohm effect created by the Abelian U(1) gauge field. The simplest non-Abelian…
We develop an optimized perturbation theory for the Ginzburg - Landau description of thermal fluctuations effects in the vortex liquids. Unlike the high temperature expansion which is asymptotic, the optimized expansion is convergent.…
We construct entire solutions of the magnetic Ginzburg-Landau equations in dimension 4 using Lyapunov-Schmidt reduction. The zero set of these solutions are close to the minimal submanifolds studied by Arezzo-Pacard\cite{Arezzo}. We also…
The Ginzburg--Landau (GL) equations of superconductivity provide a computational model for the study of magnetic flux vortices in type-II superconductors. In this article we show through numerical examples and rigorous mathematical analysis…
Thermodynamically stable vortex-antivortex structures in a quasi-two-dimensional superconductor in a tilted magnetic field are predicted. For this geometry, both orbital and spin pair-breaking effects exist, with their relative strength…
To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level…
A superconducting rod with a magnetic moment on top develops vortices obtained here through 3D calculations of the Ginzburg-Landau theory. The inhomogeneity of the applied field brings new properties to the vortex patterns that vary…
We consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions we show that wave-like solutions exist when obstacles (characterized by "holes") are present in the…
We present a geometry-based discussion of possible vortex configurations in the mixed state of anisotropic type-II superconductors. It is shown that, if energy considerations assign six nearest neighbors to each vortex, two distinct…
Theories, simulations and experiments on vortex dynamics in quasi-two-dimensional magnetic materials are reviewed. These materials can be modelled by the classical two-dimensional anisotropic Heisenberg model with XY (easy-plane) symmetry.…
We demonstrate the existence of stable time dependent solutions of the Landau-Lifshitz model with a constant external magnetic field. We find such solutions in all topological sectors, including N=0. We discuss some of their properties.
It is shown that the complex Ginzburg-Landau (CGL) equation on the real line admits nontrivial $2\pi$-periodic vortex solutions that have $2n$ simple zeros (``vortices'') per period. The vortex solutions bifurcate from the trivial solution…
Vortex solutions are topologically stable field configurations that can play an important role in condensed matter, field theory, and cosmology. We investigate vortex configuration in a 2+1 dimensional Abelian Higgs theory supplemented by…