Magnetic Fields of Vortices in a Superconducting Thin Film

The magnetic fields associated with a single superconducting vortex traversing a thin film are calculated. The formulation of Pearl, which has been used for a geometry in which for z<0 one has a vacuum and for z>0 one has superconducting material, is extended to the case of a thin film. For the thin film, the flux in the mid-plane is less than a flux quantum unless one uses a very large radius. For instance a 100 nm film with a 130 nm penetration depth (λ) has only 80% of a flux quantum within a radius of 1.5 μm = 11.5 λ. At 10 μm 96% is enclosed. The magnetic field near the surface in both geometries has a significant radial component. The fields for a vortex array are then obtained by summing the fields from nearby vortices. The measurability of the field distributions is discussed.