Abstract
We investigate vortex pinning in solutions to the Ginzburg–Landau equation. The coefficient, a(x), in the Ginzburg–Landau free energy modeling non-uniform superconductivity is nonnegative and is allowed to vanish at a finite number of points. For a sufficiently large applied magnetic field and for all sufficiently large values of the Ginzburg–Landau parameter κ=1/ε, we show that minimizers have nontrivial vortex structures. We also show the existence of local minimizers exhibiting arbitrary vortex patterns, pinned near the zeros of a(x).
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