Numerical calculations of superheating field in superconductors with nanostructured surfaces.

We report the numerical calculation of a DC superheating field H_sh by solving the Ginzburg-Landau (GL) equations for superconductors with inhomogeneous impurity concentration at the surface and superconductor-insulator-superconductor (S-I-S) multilayers. The superheating field was calculated as the field onset of instability of the Meissner state with respect to perturbations with a finite wavelength along the surface for the GL parameters κ typical of Nb and Nb₃Sn. We show that optimizing the thicknesses of the impurity diffusion layer and the overlayer in the S-I-S structure can significantly increase H_sh beyond the bulk superheating fields of both materials. For instance, a S-I-S structure comprised of a 90 nm thick Nb₃Sn overlayer on Nb can boost H_sh up to 500 mT while blocking dendritic thermomagnetic avalanches triggered by local penetration of vortices. This H_sh is about 2.2 times higher than the H_sh of Nb and ≃ 5.3 % higher than the H_sh of Nb₃Sn.