11 research outputs found
Vortices in small superconducting disks
We study the Ginzburg-Landau equations in order to describe a two-dimensional
superconductor in a bounded domain. Using the properties of a particular
integrability point () of these nonlinear equations which
allows vortex solutions, we obtain a closed expression for the energy of the
superconductor. The presence of the boundary provides a selection mechanism for
the number of vortices.
A perturbation analysis around enables us to include the
effects of the vortex interactions and to describe quantitatively the
magnetization curves recently measured on small superconducting disks.
We also calculate the optimal vortex configuration and obtain an expression
for the confining potential away from the London limit.Comment: 4 pages, to be published in Physica C (Superconductivity
Vortices in Ginzburg-Landau billiards
We present an analysis of the Ginzburg-Landau equations for the description
of a two-dimensional superconductor in a bounded domain. Using the properties
of a special integrability point of these equations which allows vortex
solutions, we obtain a closed expression for the energy of the superconductor.
The role of the boundary of the system is to provide a selection mechanism
for the number of vortices.
A geometrical interpretation of these results is presented and they are
applied to the analysis of the magnetization recently measured on small
superconducting disks. Problems related to the interaction and nucleation of
vortices are discussed.Comment: RevTex, 17 pages, 3 eps figure
Vortex nucleation through edge states in finite Bose-Einstein condensates
We study the vortex nucleation in a finite Bose-Einstein condensate. Using a
set of non-local and chiral boundary conditions to solve the
Schrdinger equation of non-interacting bosons in a rotating trap, we
obtain a quantitative expression for the characteristic angular velocity for
vortex nucleation in a condensate which is found to be 35% of the transverse
harmonic trapping frequency.Comment: 24 pages, 8 figures. Both figures and the text have been revise
Mesoscopic superconductors in the London limit: equilibrium properties and metastability
We present a study of the behaviour of metastable vortex states in mesoscopic
superconductors. Our analysis relies on the London limit within which it is
possible to derive closed analytical expressions for the magnetic field and the
Gibbs free energy. We consider in particular the situation where the vortices
are symmetrically distributed along a closed ring. There, we obtain expressions
for the confining Bean-Livingston barrier and for the magnetization which turns
out to be paramagnetic away from thermodynamic equilibrium. At low temperature,
the barrier is high enough for this regime to be observable. We propose also a
local description of both thermodynamic and metastable states based on
elementary topological considerations; we find structural phase transitions of
vortex patterns between these metastable states and we calculate the
corresponding critical fields.Comment: 24 pages, 20 figure
A dual point description of mesoscopic superconductors
We present an analysis of the magnetic response of a mesoscopic
superconductor, i.e. a system of sizes comparable to the coherence length and
to the London penetration depth. Our approach is based on special properties of
the two dimensional Ginzburg-Landau equations, satisfied at the dual point
Closed expressions for the free energy and the
magnetization of the superconductor are derived. A perturbative analysis in the
vicinity of the dual point allows us to take into account vortex interactions,
using a new scaling result for the free energy. In order to characterize the
vortex/current interactions, we study vortex configurations that are out of
thermodynamical equilibrium. Our predictions agree with the results of recent
experiments performed on mesoscopic aluminium disks.Comment: revtex, 20 pages, 9 figure