Two dimensional vortex structures in a superconductor slab at low temperatures

The dynamics of a two dimensional chain like structure of vortices is studied in the model of nonlinear time dependent Ginzburg–Landau equations (TDGL). The transition between different linear chains of vortices in a superconducting homogeneous slab with both surfaces in contact with a thin layer of metallic material is analyzed. The magnetization curve, vortex number, vortex configurations and modulus of the order parameter are studied as a function of the external magnetic field. We show how these vortex configurations are affected by the extrapolation length b (de Gennes boundary conditions), Ψ due to the proximity effects in a mesoscopic sample of area d_x × d_y, where d_y = 60ξ(0) and d_x varies discretely from 30ξ(0) to 12ξ(0). Possible connection with recent theoretical results in a two dimensional system of charged particles is discussed.