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

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.