GINZBURG-LANDAU THEORY OF VORTICES IN $d$-WAVE SUPERCONDUCTORS

TL;DR

This paper applies Ginzburg-Landau theory to analyze vortex structures and lattice arrangements in $d_{x^2-y^2}$ superconductors, revealing specific order parameter behaviors and lattice geometries near critical temperature.

Contribution

It provides a detailed theoretical description of vortex structures and lattice configurations in $d$-wave superconductors using Ginzburg-Landau theory, including comparison with experimental data.

Findings

Single vortex has a four-lobe $s$-wave structure around the core.

Vortex lattice transitions from triangular near $T_c$ to oblique at lower temperatures.

Comparison with neutron scattering data supports the theoretical model.

Abstract

Ginzburg-Landau theory is used to study the properties of single vortices and of the Abrikosov vortex lattice in a $d_{x^2-y^2}$ superconductor. For a single vortex, the $s$-wave order parameter has the expected four-lobe structure in a ring around the core and falls off like $1/r^2$ at large distances. The topological structure of the $s$-wave order parameter consists of one counter-rotating unit vortex, centered at the core, surrounded by four symmetrically placed positive unit vortices. The Abrikosov lattice is shown to have a triangular structure close to $T_c$ and an oblique structure at lower temperatures. Comparison is made to recent neutron scattering data.