Ginzburg-Landau Theory of Vortices ind-Wave Superconductors

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 counterrotating unit vortex, centered at the core, surrounded by four symmetrically placed positive unit vortices. The Abrikosov lattice varies continuously from triangular, through oblique, to square with increasing field and $s$- $d$ mixing parameter ${\epsilon }_v$. Comparison is made to recent neutron scattering data.