AC Response of Thin Film Superconductors at Various Temperatures and Magnetic Fields

The basic theory of the linear and nonlinear ac susceptibilities of type-II superconductors is outlined for various geometries, e.g. circular and elliptic disks, rings, and strips of thin films or of thicker platelets in a perpendicular magnetic field. It is shown how the linear susceptibility depends on the linear complex resistivity or on the complex penetration depth, and the nonlinear susceptibility on the nonlinear dependence of the electric field on the current density and magnetic induction. The dependence of these constitutive laws on the temperature and on various material properties like pinning forces, pinning energies, structural defects, and granularity, leads to an implicit dependence of the ac susceptibility on these parameters.Comment: Latex file and 3 postscript figures, gives 13 pages text with figures built i

Electrodynamics of Superconductors Exposed to High Frequency Fields

The electric losses in a bulk or film superconductor exposed to a parallel radio-frequency magnetic field may have three origins: In homogeneous vortex-free superconductors losses proportional to the frequency squared originate from the oscillating normal-conducting component of the charge carriers which is always present at temperatures $T>0$. With increasing field amplitude the induced supercurrents approach the depairing current at which superconductivity breaks down. And finally, if magnetic vortices can penetrate the superconductor they typically cause large losses since they move driven by the AC supercurrent.Comment: 12 pages, 18 figures, for conference proceeding

Longitudinal magnetic field increases critical current in superconducting strip

The critical state of the vortex lattice in a thin strip is considered for the case when first a perpendicular magnetic field is applied, then a longitudinal field, and then again the perpendicular field is increased. This longitudinal field can strongly enhance the critical currents in the strip since the vortices are inclined and the currents flow in the strip plane.Comment: 4 pages, 5 figures, for Low Temperature Conference LT2

Thin Ohmic or superconducting strip with an applied ac electric current

The complex impedance, currents, and electric and magnetic fields are calculated as functions of resistivity and frequency or London depth for a long thin strip with applied ac current. Both Ohmic and superconducting strips are considered. While the inductance per unit length of the strip depends on the strip length logarithmically, the sheet current, magnetic field, resistance, and magnetic susceptibility are independent of this length. It is found that the enhancement of resistance by the skin effect in thin Ohmic strips is much weaker (logarithmic) than in thick wires.Comment: 4 pages, 3 figures, for Phys. Rev.

Surface charge of a flat superconducting slab in the Meissner state

The electrostatic potential in the flat superconducting slab is evaluated in the framework of the Ginzburg-Landau theory extended by Bardeen to low temperatures. For magnetic fields below B_c1, we discuss the formation of a surface charge induced by the Bernoulli potential of the suppercurrents.Comment: 6 pages, 5 figure

Vortex induced deformation of the superconductor crystal lattice

Deformation of the superconductor crystal lattice caused by Abrikosov vortices is formulated as a response of the elastic crystal lattice to electrostatic forces. It is shown that the lattice compression is linearly proportional to the electrostatic potential known as the Bernoulli potential. Eventual consequences of the crystal lattice deformation on the effective vortex mass are discussed.Comment: 4 pages 5 figure

Thin superconductors and SQUIDs in perpendicular magnetic field

It is shown how the static and dynamic electromagnetic properties can be calculated for thin flat superconducting films of any shape and size, also multiply connected as used for SQUIDs, and for any value of the effective magnetic London penetration depth Lambda. As examples, the distributions of sheet current and magnetic field are obtained for rectangular and circular films without and with slits and holes, in response to an applied perpendicular magnetic field and to magnetic vortices moving in the film. The self energy and interaction of vortices with each other and with an applied magnetic field and/or transport current are given. Due to the long ranging magnetic stray field, these energies depend on the size and shape of the film and on the vortex position even in large films, in contrast to the situation in large bulk superconductors. The focussing of magnetic flux into the central hole of square films without and with a radial slit is compared.Comment: 12 pages, 10 figure

Vortex-vortex interaction in thin superconducting films

The properties of vortices in superconducting thin films are revisited. The interaction between two Pearl vortices in an infinite film is approximated at all distances by a simple expression. The interaction of a vortex with a regular lattice of real or image vortices is given. The two spring constants are calculated that one vortex in the vortex lattice feels when the surrounding vortices are rigidly pinned or are free. The modification of these London results by the finite size of real films is obtained. In finite films, the interaction force between two vortices is not a central force but depends on both vortex positions, not only on their distance. At the film edges the interaction energy is zero and the interaction force is peaked. Even far from the edges the vortex interaction considerably deviates from the Pearl result and is always smaller than it.Comment: 9 pages, 6 figure