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

Metastability and paramagnetism in superconducting mesoscopic disks

A projected order parameter is used to calculate, not only local minima of the Ginzburg-Landau energy functional, but also saddle points or energy barriers responsible for the metastabilities observed in superconducting mesoscopic disks (Geim et al. Nature {\bf 396}, 144 (1998)). We calculate the local minima magnetization and find the energetic instability points between vortex configurations with different vorticity. We also find that, for any vorticity, the supercurrent can reverse its flow direction on decreasing the magnetic field before one vortex can escape.Comment: Modified version as to appear in Phys. Rev. Let

Heat Capacity of Mesoscopic Superconducting Disks

We study the heat capacity of isolated giant vortex states, which are good angular momentum ($L$) states, in a mesoscopic superconducting disk using the Ginzburg-Landau (GL) theory. At small magnetic fields the $L$=0 state qualitatively behaves like the bulk sample characterized by a discontinuity in heat capacity at $T_c$. As the field is increased the discontinuity slowly turns into a continuous change which is a finite size effect. The higher $L$ states show a continuous change in heat capacity at $T_c$ at all fields. We also show that for these higher $L$ states, the behavior of the peak position with change in field is related to the paramagnetic Meissner effect (irreversible) and can lead to an unambiguous observation of positive magnetization in mesoscopic superconductors.Comment: Final versio

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

Poincare Polynomials and Level Rank Dualities in the N=2N=2 Coset Construction

We review the coset construction of conformal field theories; the emphasis is on the construction of the Hilbert spaces for these models, especially if fixed points occur. This is applied to the $N=2$ superconformal cosets constructed by Kazama and Suzuki. To calculate heterotic string spectra we reformulate the Gepner con- struction in terms of simple currents and introduce the so-called extended Poincar\'e polynomial. We finally comment on the various equivalences arising between models of this class, which can be expressed as level rank dualities. (Invited talk given at the III. International Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June 1993. To appear in Theor. Math. Phys.)Comment: 14 pages in LaTeX, HD-THEP-93-4

Vortex phase diagram for mesoscopic superconducting disks

Solving numerically the 3D non linear Ginzburg-Landau (GL) equations, we study equilibrium and nonequilibrium phase transitions between different superconducting states of mesoscopic disks which are thinner than the coherence length and the penetration depth. We have found a smooth transition from a multi-vortex superconducting state to a giant vortex state with increasing both the disk thickness and the magnetic field. A vortex phase diagram is obtained which shows, as function of the magnetic field, a re-entrant behavior between the multi-vortex and the giant vortex state.Comment: 5 figures (post script files) include

Hysteresis in mesoscopic superconducting disks: the Bean-Livingston barrier

The magnetization behavior of mesoscopic superconducting disks can show hysteretic behavior which we explain by using the Ginzburg-Landau (GL) theory and properly taking into account the de-magnetization effects due to geometrical form factors. In large disks the Bean-Livingston surface barrier is responsible for the hysteresis. While in small disks a volume barrier is responsible for this hysteresis. It is shown that although the sample magnetization is diamagnetic (negative), the measured magnetization can be positive at certain fields as observed experimentally, which is a consequence of the de-magnetization effects and the experimental set up.Comment: Latex file, 4 ps file

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

Suppression of Superconductivity in Mesoscopic Superconductors

We propose a new boundary-driven phase transition associated with vortex nucleation in mesoscopic superconductors (of size of the order of, or larger than, the penetration depth). We derive the rescaling equations and we show that boundary effects associated with vortex nucleation lowers the conventional transition temperature in mesoscopic superconductors by an amount which is a function of the size of the superconductor. This result explains recent experiments in small superconductors where it was found that the transition temperature depends on the size of the system and is lower than the critical Berezinsk\u{i}-Kosterlitz-Thouless temperature.Comment: To appear in Phys. Rev. Lett. Vol. 86 (15 Jan. 2001