Properties of the flux-line lattice in anisotropic superconductors nearHc2

Using anisotropic Ginzburg-Landau (GL) equations based upon a tensor effective-mass approximation, we study the vortex lattice geometry near the upper critical field ${\mathit{H}}_{\mathit{c}2}$. We employ a scaling technique to reduce the first GL equation to isotropic form. This permits simple evaluation of the angular dependence of the upper critical field for arbitrary mass anisotropy. Although the mass tensor cannot be scaled out of the second GL equation, the two equations may be solved and the free energy evaluated. In the high-κ limit appropriate, e.g., to the new high-temperature superconductors, the geometry of the fluxoid lattice is found to be hexagonal in scaled coordinates but with a preferred orientation relative to the underlying crystallographic axes. The internal magnetic fields both parallel and perpendicular to the vortex axis are determined for the special case of uniaxial anisotropy.