FAST CONVERGENT FREE-ENERGY EXPANSION FOR UNIAXIAL SUPERCONDUCTORS IN THE LONDON APPROXIMATION

A fast convergent expansion for the free energy of uniaxial superconductors in the London approximation is obtained here. The free energy formula is invariant under different choices of unit cell describing the same physical vortex lattice. To illustrate the method some numerical calculations are done in the case of one vortex per unit cell. In the limit of high values of the magnetic induction the resulting vortex pattern approaches the distorted triangular lattice of Campbell, Doria and Kogan. The author find that for low enough values of the magnetic induction, any two vortices located in adjacent chains are highly uncorrelated. Numerical evidence shows the existence of a rectangular lattice configuration that extremizes the free energy for any orientation of the magnetic induction.