Structure of the Abrikosov vortex lattice in a thin superconducting film in a parallel magnetic field

The structure of a vortex lattice in thin (d<λ, where d is the film thickness and λ is the London penetration depth) superconducting films is investigated in a magnetic field parallel to the film surface. It is shown that the stable configuration has the form of discrete vortex rows whose number changes discretely with an increase in the applied magnetic field. The entry fields H _c1 ^(N) (d) for vortex rows are calculated for N=1, 2. It is shown that the structural transition in the vortex ensemble is a second-order phase transition. A simpler method (as compared to the Monte Carlo technique) is proposed for calculating the vortex lattice parameters.