Vortices and pinning effects for the Ginzburg‐Landau model in multiply connected domains

We consider the two‐dimensional Ginzburg‐Landau model with magnetic field for a superconductor with a multiply connected cross section. We study energy minimizers in the London limit as the Ginzburg‐Landau parameter κ = 1/ϵ → ∞ to determine the number and asymptotic location of vortices. We show that the holes act as pinning sites, acquiring nonzero winding for bounded fields and attracting all vortices away from the interior for fields up to a …