Numerical Method for Zero-Temperature Vortex-Line Phase Diagrams

Abstract

A numerical method to calculate equilibrium vortex-line configurations in bulk anisotropic type-II superconductors, at zero temperature, placed in an external magnetic field is introduced and applied to two physical problems. The method is designed to search for the minimum of the Gibbs free-energy in the London approximation and assumes only that the vortex lines are straight and arranged in a periodic lattice. Based on these assumptions a simulated annealing algorithm is developed to find the vortex-line-lattice unit cell shape, and vortex-line positions within it. This algorithm is made fast and accurate by the use of a rapidly converging series to calculate the lattice sums entering the vortex-vortex interaction energy. The method's accuracy is illustrated by calculating the magnetic induction versus applied field curve for an isotropic superconductor. The method is applied to a superconductor with a square lattice of columnar defects to study selected regions of the zero-temperature-phase diagram where vortex-line-lattices commensurate with the columnar defect lattice exist.