Properties of the Ideal Ginzburg-Landau Vortex Lattice

TL;DR

This paper provides detailed calculations of the magnetic properties of ideal type-II superconductor vortex lattices across a wide range of parameters, comparing exact results with common approximations.

Contribution

It offers comprehensive Ginzburg-Landau theory calculations for vortex lattice magnetic fields and magnetization, including exact solutions and improved approximations.

Findings

Exact magnetic field B(x,y) and magnetization M(H, kappa) are derived.

Comparison shows some approximate methods deviate significantly from exact results.

Analytical formulas and interpolations are provided for practical use.

Abstract

The magnetization curves M(H) for ideal type-II superconductors and the maximum, minimum, and saddle point magnetic fields of the vortex lattice are calculated from Ginzburg-Landau theory for the entire ranges of applied magnetic fields Hc1 <= H < Hc2 or inductions 0 <= B < Hc2 and Ginzburg-Landau parameters sqrt(1/2) <= kappa <= 1000. Results for the triangular and square flux-line lattices are compared with the results of the circular cell approximation. The exact magnetic field B(x,y) and magnetization M(H, kappa) are compared with often used approximate expressions, some of which deviate considerably or have limited validity. Useful limiting expressions and analytical interpolation formulas are presented.