Magnetic and transport currents in thin film superconductors of arbitrary shape within the London approximation

Abstract

We present a numerical method to calculate the current distribution and the magnetic field in a superconducting thin plate within the London approximation. The superconductor can have any two-dimensional shape, including multiply connected ones. The modeling can take into account transport currents fed on the superconductor and externally applied fields, and is valid for any value of the London penetration depth λ. From this modeling, we present current and field distributions for several geometries of the superconductor (including corners, turns, and holes), comparing them with these of a straight strip and with previous results in some limits. We show how the current density accumulates in the inner corners of a turn and how this accumulation depends on λ. We also study how far the presence of a turn or hole in a straight strip modifies the current (and field) distribution observing significant differences depending on λ, on the geometry of the turns and on the external conditions to which the superconductor is subjected. All these results may have implications in the design of single photon detectors, superconducting based mass spectrometers, as well as in the ability of tuning magnetic traps using thin superconducting films, among other applications.