Maximum screening fields of superconducting multilayer structures

It is shown that a multilayer comprised of alternating thin superconducting and insulating layers on a thick substrate can fully screen the applied magnetic field exceeding the superheating fields $H_s$ of both the superconducting layers and the substrate, the maximum Meissner field is achieved at an optimum multilayer thickness. For instance, a dirty layer of thickness $\sim 0.1\; \mu$m at the Nb surface could increase $H_s\simeq 240$ mT of a clean Nb up to $H_s\simeq 290$ mT. Optimized multilayers of Nb$_3$Sn, NbN, some of the iron pnictides, or alloyed Nb deposited onto the surface of the Nb resonator cavities could potentially double the rf breakdown field, pushing the peak accelerating electric fields above 100 MV/m while protecting the cavity from dendritic thermomagnetic avalanches caused by local penetration of vortices.