Vortex pinning by cylindrical defects in type-II superconductors: Numerical solutions to the Ginzburg-Landau equations

We numerically integrate the one-dimensional, cylindrically symmetric Ginzburg-Landau equations to calculate the spatial variation of the order parameter and supercurrents for a vortex trapped by a cylindrical defect. We use the resulting field distributions to estimate the pinning energy, and make use of the vortex/two-dimensional boson analogy to calculate the depinning temperature. The microscopic behavior oi the fields depends on the size, and the conductivity of the cylindrical defect appears to be important for the pinning.