73 research outputs found

### Spontaneous breaking of axial symmetry for Schroedinger's equation in the presence of a magnetic field

For appropriate parameters, the ground state for the Schroedinger and Ampere
coupled equations in a cylindric domain does not have axial symmetry.Comment: 2 page

### Dependence of the vortex configuration on the geometry of mesoscopic flat samples

The influence of the geometry of a thin superconducting sample on the
penetration of the magnetic field lines and the arrangement of vortices are
investigated theoretically. We compare superconducting disks, squares and
triangles with the same surface area having nonzero thickness. The coupled
nonlinear Ginzburg-Landau equations are solved self-consistently and the
important demagnetization effects are taken into account. We calculate and
compare quantities like the free energy, the magnetization, the Cooper-pair
density, the magnetic field distribution and the superconducting current
density for the three geometries. For given vorticity the vortex lattice is
different for the three geometries, i.e. it tries to adapt to the geometry of
the sample. This also influences the stability range of the different vortex
states. For certain magnetic field ranges we found a coexistence of a giant
vortex placed in the center and single vortices toward the corners of the
sample. Also the H-T phase diagram is obtained.Comment: 9 pages, 17 figures (submitted to Phys. Rev. B

### Vortex Matter in Mesoscopic Superconducting Disks and Rings

Phase transitions between different (i.e. giant and multi-vortex)
superconducting states and between the superconducting-normal state of
mesoscopic disks and rings are studied in the presence of an external magnetic
field by solving the two non-linear Ginzburg-Landau equations
self-consistently. The flux through a circular disk with a hole in the middle
is not quantized.Comment: 8 pages, 10 figures; to appear in Physica C (proceedings of the
conference on Vortex matter, Crete (september 1999

### Superconducting properties of mesoscopic cylinders with enhanced surface superconductivity

The superconducting state of an infinitely long superconducting cylinder
surrounded by a medium which enhances its superconductivity near the boundary
is studied within the nonlinear Ginzburg-Landau theory. This enhancement can be
due to the proximity of another superconductor or due to surface treatment.
Quantities like the free energy, the magnetization and the Cooper-pair density
are calculated. Phase diagrams are obtained to investigate how the critical
field and the critical temperature depend on this surface enhancement for
different values of the Ginzburg-Landau parameter \kappa. Increasing the
superconductivity near the surface leads to higher critical fields and critical
temperatures. For small cylinder diameters only giant vortex states nucleate,
while for larger cylinders multivortices can nucleate. The stability of these
multivortex states also depends on the surface enhancement. For type-I
superconductors we found the remarkable result that for a range of values of
the surface extrapolation length the superconductor can transit from the
Meissner state into superconducting states with vorticity L > 1. Such a
behaviour is not found for the case of large \kappa, i.e. type-II
superconductivity.Comment: submitted to Phys. Rev.

### Vortex states in superconducting rings

The superconducting state of a thin superconducting disk with a hole is
studied within the non-linear Ginzburg-Landau theory in which the
demagnetization effect is accurately taken into account. We find that the flux
through the hole is not quantized, the superconducting state is stabilized with
increasing size of the hole for fixed radius of the disk, and a transition to a
multi-vortex state is found if the disk is sufficiently large. Breaking the
circular summetry through a non central location of the hole in the disk
enhances the multi-vortex state.Comment: 11 pages, 23 figures (postscript). To appear in Physical Review B,
Vol. 61 (2000

### Mesoscopic superconducting disks

Using the non-linear Ginzburg-Landau (GL) eqs. type I superconducting disks
of finite radius ($R$) and thickness ($d$) are studied in a perpendicular
magnetic field. Depending on $R$ and $d$, first or second order phase
transitions are found for the normal to superconducting state. For sufficiently
large $R$ several transitions in the superconducting phase are found
corresponding to different angular momentum giant vortex states. In increasing
magnetic field the superconductor is in its ground state, while in field down
sweep it is possible to drive the system into metastable states. We also
present a quantitative analysis of the relation between the detector output and
the sample magnetization. The latter, and the incorporation of the finite
thickness of the disks, are essential in order to obtain quantitative agreement
with experiment.Comment: A brief review with new result

### 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
$(\kappa = \frac{1}{\sqrt{2}}).$ 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

### Structure and Melting of Two-Species Charged Clusters in a Parabolic Trap

We consider a system of charged particles interacting with an unscreened
Coulomb repulsion in a two-dimensional parabolic confining trap. The static
charge on a portion of the particles is twice as large as the charge on the
remaining particles. The particles separate into a shell structure with those
of greater charge situated farther from the center of the trap. As we vary the
ratio of the number of particles of the two species, we find that for certain
configurations, the symmetry of the arrangement of the inner cluster of
singly-charged particles matches the symmetry of the outer ring of
doubly-charged particles. These matching configurations have a higher melting
temperature and a higher thermal threshold for intershell rotation between the
species than the nonmatching configurations.Comment: 4 pages, 6 postscript figure

### Enhanced stability of the square lattice of a classical bilayer Wigner crystal

The stability and melting transition of a single layer and a bilayer crystal
consisting of charged particles interacting through a Coulomb or a screened
Coulomb potential is studied using the Monte-Carlo technique. A new melting
criterion is formulated which we show to be universal for bilayer as well as
for single layer crystals in the case of (screened) Coulomb, Lennard--Jones and
1/r^{12} repulsive inter-particle interactions. The melting temperature for the
five different lattice structures of the bilayer Wigner crystal is obtained,
and a phase diagram is constructed as a function of the interlayer distance. We
found the surprising result that the square lattice has a substantial larger
melting temperature as compared to the other lattice structures. This is a
consequence of the specific topology of the defects which are created with
increasing temperature and which have a larger energy as compared to the
defects in e.g. a hexagonal lattice.Comment: Accepted for publication in Physical Review

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