Vortices in thin superconducting disks, plates, and SQUIDs
Ernst Helmut Brandt*
Max-Planck-Institute for Metals Research, D-70506 Stuttgart, Germany
In the first half of this talk, detailed computations of the periodic vortex lattice in films of
arbitrary thickness from Ginzburg-Landau theory are presented, when these vortices are
perpendicular to the film. The magnetic field inside and outside the film, the current density,
order parameter, energies, and shear modulus of the triangular vortex lattice are calculated for
the entire ranges of the magnetic induction B, GL parameter κ, and film thickness d by
generalizing a former Fourier-series method from the bulk to films. While for thick films and
bulk superconductors the shear modulus is formally negative when κ < 0.707, for thin films
the shear modulus can remain positive even for type-I superconductors with κ < 0.707.
In the second half of this talk the macroscopic magnetic field, sheet current density, trapped
magnetic flux, self-inductance, and energies are computed for thin superconductor plates or
films of rectangular or circular shape, which may contain a hole and a slit as used for
SQUIDs. These flat films are exposed to a perpendicular magnetic field, may carry applied
current, and may contain one or more vortices. The electrodynamic properties are computed
from Maxwell-London theory for zero or finite effective magnetic penetration depth Λ=λ2/d.
Finally, the problem of the Bean critical state in a thick type-II superconducting strip in
oblique magnetic field is discussed.
References
E. H. Brandt, Phys. Rev. Lett. 78, 2208 (1997).
E. H. Brandt, Phys. Rev. Rev. B 68, 054506 (2003), and to be published.
E. H. Brandt, Phys. Rev. Rev. B 64, 024505 (2001), and to be published.
E. H. Brandt and J. R. Clem, Phys. Rev. Rev. B 69, 184509 (2004).
G. P. Mikitik, E. H. Brandt, and M. Indenbom, Phys. Rev. Rev. B 70, 014520 (2004).
*
E-mail: ehb@mf.mpg.de