Flux pinning by thin planar defects

Abstract

Planar defects, specifically grain boundaries, are now recognized as a major source of flux pinning in many materials, including the commercial A-15 superconductors. Unfortunately little theoretical attention has been devoted to the interaction between a planar pinning centre and the flux line lattice (FLL) of a type II superconductor. A Ginzburg-Landau perturbational approach is used here to calculate the pinning force per unit area exerted by a thin isolated planar defect upon the FLL. The pinning force is considered to arise from electron scattering at the defect plane, which creates a perturbation in the Ginzburg-Landau parameter,κ. The method of approach is of general applicability, however, and is easily adapted to other pinning mechanisms encompassed by the perturbational formalism. Second order terms in the FLL energy are retained, as well as all significant higher order terms in the Fourier transforms both of the superconducting electron density ¦ψ¦2, and of ¦ψ¦4. It is shown that a large error results, except at very high fields, if the above terms are ignored. The functional dependence of the elementary pinning force on temperature and field are shown to vary somewhat with the nature of the material and the pinning defect.