Saddle point states and energy barriers for vortex entrance and exit in superconducting disks and rings

The transitions between the different vortex states of thin mesoscopic superconducting disks and rings are studied using the non-linear Ginzburg-Landau functional. They are saddle points of the free energy representing the energy barrier which has to be overcome for transition between the different vortex states. In small superconducting disks and rings the saddle point state between two giant vortex states, and in larger systems the saddle point state between a multivortex state and a giant vortex state and between two multivortex states is obtained. The shape and the height of the nucleation barrier is investigated for different disk and ring configurations.Comment: 10 pages, 18 figure

Induced order and reentrant melting in classical two-dimensional binary clusters

A binary system of classical charged particles interacting through a dipole repulsive potential and confined in a two-dimensional hardwall trap is studied by Brownian dynamics simulations. We found that the presence of small particles \emph{stabilizes} the angular order of the system as a consequence of radial fluctuations of the small particles. There is an optimum in the increased rigidity of the cluster as function of the number of small particles. The small (i.e. defect) particles melt at a lower temperature compared to the big particles and exhibit a \emph{reentrant} behavior in its radial order that is induced by the intershell rotation of the big particles.Comment: 7 pages, 3 figure

On the Brauer groups of symmetries of abelian Dijkgraaf-Witten theories

Symmetries of three-dimensional topological field theories are naturally defined in terms of invertible topological surface defects. Symmetry groups are thus Brauer-Picard groups. We present a gauge theoretic realization of all symmetries of abelian Dijkgraaf-Witten theories. The symmetry group for a Dijkgraaf-Witten theory with gauge group a finite abelian group $A$, and with vanishing 3-cocycle, is generated by group automorphisms of $A$, by automorphisms of the trivial Chern-Simons 2-gerbe on the stack of $A$-bundles, and by partial e-m dualities. We show that transmission functors naturally extracted from extended topological field theories with surface defects give a physical realization of the bijection between invertible bimodule categories of a fusion category and braided auto-equivalences of its Drinfeld center. The latter provides the labels for bulk Wilson lines; it follows that a symmetry is completely characterized by its action on bulk Wilson lines.Comment: 21 pages, 9 figures. v2: Minor changes, typos corrected and references added. v3: Typos correcte

From non-semisimple Hopf algebras to correlation functions for logarithmic CFT

We use factorizable finite tensor categories, and specifically the representation categories of factorizable ribbon Hopf algebras H, as a laboratory for exploring bulk correlation functions in local logarithmic conformal field theories. For any ribbon Hopf algebra automorphism omega of H we present a candidate for the space of bulk fields and endow it with a natural structure of a commutative symmetric Frobenius algebra. We derive an expression for the corresponding bulk partition functions as bilinear combinations of irreducible characters; as a crucial ingredient this involves the Cartan matrix of the category. We also show how for any candidate bulk state space of the type we consider, correlation functions of bulk fields for closed oriented world sheets of any genus can be constructed that are invariant under the natural action of the relevant mapping class group.Comment: 41 pages, several figures. version 2: typos corrected, bibliography updated, introduction extended, a few minor clarifications adde

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

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

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.

Classical double-layer atoms: artificial molecules

The groundstate configuration and the eigenmodes of two parallel two-dimensional classical atoms are obtained as function of the inter-atomic distance (d). The classical particles are confined by identical harmonic wells and repel each other through a Coulomb potential. As function of d we find several structural transitions which are of first or second order. For first (second) order transitions the first (second) derivative of the energy with respect to d is discontinuous, the radial position of the particles changes discontinuously (continuously) and the frequency of the eigenmodes exhibit a jump (one mode becomes soft, i.e. its frequency becomes zero).Comment: 4 pages, RevTex, 5 ps figures, to appear in Phys.Rev.Let

Vortex structure of thin mesoscopic disks in the presence of an inhomogeneous magnetic field

The vortex states in a thin mesoscopic disk are investigated within the phenomenological Ginzburg-Landau theory in the presence of different ''model'' magnetic field profiles with zero average field which may result from a ferromagnetic disk or circulating currents in a loop near the superconductor. We calculated the dependences of both the ground and metastable states on the magnitude and shape of the magnetic field profile for different values of the order parameter angular moment, i.e. the vorticity. The regions of existence of the multi-vortex state and the giant vortex state are found. We analysed the phase transitions between these states and studied the contribution from ring-shaped vortices. A new transition between different multi-vortex configurations as the ground state is found. Furthermore, we found a vortex state consisting of a central giant vortex surrounded by a collection of anti-vortices which are located in a ring around this giant vortex. The limit to a disk with an infinite radius, i.e. a film, will also be discussed. We also extended our results to ''real'' magnetic field profiles and to the case in which an external homogeneous magnetic field is present.Comment: 17 pages, 23 figures. Submitted to PR