Ginzburg-Landau theory of the Abrikosov lattice in a d-wave superconductor

We consider the Ginzburg-Landau free energy for the case of coexisting s- and d-wave order parameters, coupled to a gauge field, for a system in which the minimum energy state in the absence of magnetic fields is uniform d-wave. The eigenvalue equation arising from the coupled Ginzburg-Landau equations, in the presence of a uniform magnetic field, is implicitly non-linear and has no obvious closed-form solution. We employ a simple variational …