Supercurrents and vortices in SQUIDs and films of various shapes

Meissner transport current in flat films of arbitrary shape and a magnetic trap for cold atoms

“…are the usual 2D divergence and curl operators, respectively, and τ is the counter-clockwise length parameterization of . The boundary condition makes sense because J n dτ = 0; see [22,23] for a discussion on the properties of the stream function. Substituting (5) into (3), we can rewrite (4) as the following integral equation for the stream function:…”

“…Since modeling Meissner's state for thin films in an external magnetic field has already been performed, see [21][22][23], in the examples below we consider only the case of transport current and assume the external field H ext,z is zero. Of course, in the general case, the solution is the sum of solutions to problems with I = 0, H ext,z = 0 and I = 0, H ext,z = 0.…”

“…Computing current density distribution in multiply connected superconducting films is needed for films with natural or artificially created defects [24,25], SQUIDs [22,23], some types of atom chips [26], etc. As an example, we present the calculated current density in a film with one hole (figure 3).…”

Magnetic field profile of a mesoscopic SQUID-shaped superconducting film

“…Since within the London model the order parameter is assumed to be constant everywhere, one can reasonably expect that results arising from such a treatment will be less accurate than those obtained from a more comprehensive theory, such as the one employed here. To allow a direct comparison of our results with those of [6,7], one has to consider that Brandt did not introduce the explicit temperature dependence of λ(T), which can be mimicked by choosing T = 0, in which case the TDGL equations have the same form as those obtained using ξ(T) as the unit length. For this reason, the results presented in figures 2-6 refer to T = 0.…”

“…Thus, using the Bean approach, they obtained an anisotropic relaxation of the internal field and sheet currents over the sample. Some studies by Brandt [6,7], and by Clem and Brandt [8], described the distribution of the internal field and the sheet currents in thin films shaped in the so-called SQUID geometry, employing some variations for the cross section of the sample. The authors considered that finite films could be described by the London theory, expressing the sheet currents and part of the coupling flux between the vortices and the holes or slits, by a stream function.…”