Flux pinning by small perturbations in the superconducting order parameter in type-II superconductors

From a first-order perturbation of the Ginzburg–Landau free energy, the effects of local variation of the upper critical field H c2 and Ginzburg–Landau parameter κ are combined. The interaction energy ∼ |ψ|2[1 – |ψ|2] thus obtained, where |ψ| is the superconducting order parameter, varies locally. The elementary pinning force f p is calculated from the interaction energy as a function of the magnetic induction B, and is seen to be in good agreement with experimental results for several flux-pinning systems.