Arbitrary $n$ ‐vortex self‐duality solutions to the Ginzburg–Landau equations satisfying normal state conditions at infinity

Abstract

It is well known that, when the Ginzburg–Landau parameter $\kappa=1/\sqrt{2}$ , the second‐order Ginzburg–Landau equations may be reduced to the first‐order Bogomolnyi equations. It is established in this critical case that, for any given set of vortex locations and orders, these equations possess a unique solution which tends to the purely superconducting state at infinity. In the present contribution we focus on cases in which normal state conditions at infinity are imposed. It is found that, for any given set of vortex locations and orders, an infinite number of solutions satisfying such conditions at infinity exist.