Surface barrier in mesoscopic type-I and type-II superconductors

We study the surface barrier for magnetic-field penetration in mesoscopic samples of both type-I and type-II superconductors. Our results are obtained from numerical simulations of the time-dependent Ginzburg-Landau equations. We calculate the dependence of the first field for flux penetration (Hₚ) with the Ginzburg-Landau parameter (κ) observing an increase of Hₚ with decreasing {κ} for a superconductor-insulator boundary condition [(∇-iA)Ψ|ₙ=0] while for a superconductor-normal boundary condition (approximated by the limiting case of Ψ|S=0) Hₚ has a smaller value independent of {κ} and proportional to Hc. We study the magnetization curves and penetration fields at different sample sizes and for square and thin-film geometries. For small mesoscopic samples we study the peaks and discontinuous jumps found in the magnetization as a function of magnetic field. To interpret these jumps we consider that vortices located inside the sample induce a reinforcement of the surface barrier at fields greater than the first penetration field Hₚ₁. This leads to multiple penetration fields Hₚᵢ=Hₚ₁,Hₚ₂,Hₚ₃, for vortex entrance in mesoscopic samples. We study the dependence on sample size of the penetration fields Hₚᵢ. We explain these multiple penetration fields, extending the usual Bean-Livingston analysis by considering the effect of vortices inside the superconductor and the finite size of the sample.