Properties of mesoscopic superconducting thin-film rings. London approach

Superconducting thin-film rings smaller than the film penetration depth (the Pearl length) are considered. The current distribution, magnetic moment, and thermodynamic potential $\mathcal{F}(H,N,v)$ for a flat, washer-shaped annular ring in a uniform applied field $H$ perpendicular to the film are solved analytically within the London approach for a state with winding number $N$ and a vortex at radius $v$ between the inner and outer radii.