Numerical Method for Zero-Temperature Vortex-Line Phase Diagrams

TL;DR

This paper introduces a fast numerical method using simulated annealing to determine equilibrium vortex-line configurations in anisotropic type-II superconductors at zero temperature, accounting for vortex interactions and lattice structures.

Contribution

A novel numerical approach employing simulated annealing for calculating vortex-line-lattice configurations in superconductors at zero temperature, with improved speed and accuracy.

Findings

Accurately calculated magnetic induction versus applied field curve.

Identified vortex-lattice phases in superconductors with columnar defects.

Demonstrated the method's effectiveness in complex vortex lattice scenarios.

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.