Ginzburg-Landau Vortex Lattice in Superconductor Films of Finite Thickness

TL;DR

This paper solves the Ginzburg-Landau equations for vortex lattices in superconducting films of finite thickness, providing detailed 3D field and order parameter profiles across various conditions.

Contribution

It presents a comprehensive solution for vortex lattices in finite-thickness superconducting films, including surface effects and elastic properties, across a wide parameter range.

Findings

Surface variation of the order parameter is minimal (~0.01).

Surface energy of the film is small.

Shear modulus c66 in thin films matches bulk values at large kappa.

Abstract

The Ginzburg-Landau equations are solved for ideally periodic vortex lattices in superconducting films of arbitrary thickness in a perpendicular magnetic field. The order parameter, current density, magnetic moment, and the 3-dimensional magnetic field inside and outside the film are obtained in the entire ranges of the applied magnetic field, Ginzburg Landau parameter kappa, and film thickness. The superconducting order parameter varies very little near the surface (by about 0.01) and the energy of the film surface is small. The shear modulus c66 of the triangular vortex lattice in thin films coincides with the bulk c66 taken at large kappa. In thin type-I superconductor films with kappa < 0.707, c66 can be positive at low fields and negative at high fields.