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Nielsen-Olesen vortices for large Ginzburg-Landau parameter

Using analytic and numerical techniques Nielsen-Olesen vortices, which in the context of Ginzburg-Landau theory are known as Abrikosov vortices of type-II superconductors, are studied for large Ginzburg-Landau parameter $λ$. We show that their energy is equal to $(πn^2 /2)\logλ$ to leading order, where $n$ is the winding number of the vortex, and find that the limit of the gauge field can be expressed in terms of the modified Bessel function $K_1$. The leading terms of the asymptotic expansion of the solution are given, and the different contributions to the energy are analyzed.