Ginzburg-Landau vortex lattice in superconductor films of finite thickness

The Ginzburg-Landau equations are solved for ideally periodic vortex lattices in superconducting films of arbitrary thickness in a perpendicular magnetic field. The order parameter, current density, magnetic moment, and the three-dimensional magnetic field inside and outside the film are obtained in the entire ranges of the applied magnetic field, Ginzburg-Landau parameter κ, and film thickness. The superconducting order parameter varies very little near the surface (≈1%) and the energy of the film surface is small. The shear modulus c₆₆ of the triangular vortex lattice in thin films coincides with the bulk c₆₆ taken at large κ. In thin type-I superconductor films with κ<1∕√2,0.2em0exc₆₆ can be positive at low fields and negative at high fields. The magnetization of thin films at small applied fields is enhanced beyond its bulk value -Hc1 due to the energy of the magnetic stray field.