The Vortex Lattice in Ginzburg-Landau Superconductors

Abrikosov's solution of the linearized Ginzburg-Landau theory describing a periodic lattice of vortex lines in type-II superconductors at large inductions, is generalized to non-periodic vortex arrangements, e.g., to lattices with a vacancy surrounded by relaxing vortices and to periodically distorted lattices that are needed in the nonlocal theory of elasticity of the vortex lattice. Generalizations to lower magnetic inductions and to three-dimensional arrangements of curved vortex lines are also given. Finally, it is shown how the periodic vortex lattice can be computed for bulk superconductors and for thick and thin films in a perpendicular field for all inductions B and Ginzburg-Landau parameters kappa.