  It is well-known that under suitable hypotheses, for a sequence of solutions
of the (simplified) Ginzburg-Landau equations $-\Delta u_\varepsilon
+\varepsilon^{-2}(|u_\varepsilon|^2-1)u_\varepsilon = 0$, the energy and
vorticity concentrate as $\varepsilon\to 0$ around a codimension $2$ stationary
varifold -- a (measure theoretic) minimal surface. Much less is known about the
question of whether, given a codimension $2$ minimal surface, there exists a
sequence of solutions for which the given minimal surface is the limiting
concentration set. The corresponding question is very well-understood for
minimal hypersurfaces and the scalar Allen-Cahn equation, and for the
Ginzburg-Landau equations when the minimal surface is locally area-minimizing,
but otherwise quite open. We consider this question on a $3$-dimensional closed
Riemannian manifold $(M,g)$, and we prove that any embedded nondegenerate
closed geodesic can be realized as the asymptotic energy/vorticity
concentration set of a sequence of solutions of the Ginzburg-Landau equations.
