Theory of the coupling force in magnetically coupled type-II superconducting films

A pair of infinite type-II superconducting films with thicknesses dₚ and dₛ and penetration depths λₚ and λₛ separated by an insulating layer of thickness dᵢ is assumed to contain in the primary film a triangular vortex lattice, initially in perfect registry directly below an identical lattice in the secondary film. A theory is developed for the coupling force exerted upon a secondary vortex by the primary-vortex lattice as a function of the displacement of the primary lattice relative to the secondary lattice. The theory is based upon a London model of the vortex line, modified to account for vortex-core effects. The theoretical maximum coupling force is largest at low flux density, where it has a value of order φ₀²8π²ρeff², where φ₀=hc/2e and ρeff=dᵢ+λₚcoth(dₚλₚ)+λₛcoth(dₛλₛ).