Numerical studies on the effect of normal-metal coatings on the magnetization characteristics of type-II superconductors

Magnetic properties of superconductors coated with metals of arbitrary resistivity ρ_N are calculated using the time-dependent Ginzburg-Landau equations in which both T_c and ρ_N vary. As ρ_N in the coating is reduced, the initial vortex penetration field H_p(ρ_N) does not decrease monotonically from the insulating (Matricon) limit to the extreme metallic (Bean-Livingston) limit, but has a minimum value H_p(min) below the extreme metallic value. The minimum occurs because the barrier is weakened by proximity-effect penetration of superelectrons into the coating which only occurs at finite resistivity. In an applied magnetic field, local depressions in ψ nucleate in the coating which do not have the well-known quantum of magnetic flux (h∕2e) until they have crossed the coating and entered the interior of the superconductor. When T=0 and T_c of the normal metal coating is zero, the minimum vortex penetration field H_p(min)≈0.76κ^−1.17H_c2 which occurs for a coating resistivity ρ_N≈1.1κ^−0.6ρ_S. For T>0 the minimum is attenuated. Adding a thick weakly superconducting S^′ layer between the superconductor and normal metal coating reduces the irreversibility markedly.