We calculate a low-frequency surface impedance of a dirty, s-wave superconductor with an imperfect surface incorporating either a thin layer with a reduced pairing constant or a thin, proximitycoupled normal layer. Such structures model realistic surfaces of superconducting materials which can contain oxide layers, absorbed impurities or nonstoichiometric composition. We solved the Usadel equations self-consistently and obtained spatial distributions of the order parameter and the quasiparticle density of states which then were used to calculate a low-frequency surface resistance Rs(T ) and the magnetic penetration depth λ(T ) as functions of temperature in the limit of local London electrodynamics. It is shown that the imperfect surface in a single-band s-wave superconductor results in a non-exponential temperature dependence of Z(T ) at T ≪ Tc which can mimic the behavior of multiband or d-wave superconductors. The imperfect surface and the broadening of the gap peaks in the quasiparticle density of states N (ǫ) in the bulk give rise to a weakly temperaturedependent residual surface resistance. We show that the surface resistance can be optimized and even reduced below its value for an ideal surface by engineering N (ǫ) at the surface using pairbreaking mechanisms, particularly, by incorporating a small density of magnetic impurities or by tuning the thickness and conductivity of the normal layer and its contact resistance. The results of this work address the limit of Rs in superconductors at T ≪ Tc, and the ways of engineering the optimal density of states by surface nano-structuring and impurities to reduce losses in superconducting micro-resonators, thin film strip lines, and radio frequency cavities for particle accelerators.

A multilayered structure with a single superconductor layer and a single insulator layer formed on a bulk superconductor is studied. General formulae for the vortex-penetration field of the superconductor layer and the magnetic field on the bulk superconductor, which is shielded by the superconductor and insulator layers, are derived with a rigorous calculation of the magnetic field attenuation in the multilayered structure. The achievable peak surface field depends on the thickness and its material of the superconductor layer, the thickness of the insulator layer and material of the bulk superconductor. The calculation shows a good agreement with an experimental result. A combination of the thicknesses of superconductor and insulator layers to enhance the field limit can be given by the formulae for any given materials.Technologies to fabricate the superconducting RF cavities made of Nb have been advanced. The maximum accelerating gradient E acc of the TESLA type 1.3 GHz 9cell cavities during performance tests in vertical cryostats regularly exceed 35 MV/m at several laboratories. The gradient record had been increasing and recently two 9cell cavities made from large grain Nb reached 45 MV/m at DESY 1 . Further high gradients, however, would not be expected because their gradients are thought to be close to the empirical limit imposed by the thermodynamic critical field ≃ 200 mT of Nb 2 . A. Gurevich suggested 3,4 that a multilayered nanoscale coating on Nb cavity may push up the RF breakdown field to the level of the vortex-penetration field of the coating materials at which the Bean-Livingston surface barrier 5 disappears. While some experimental studies have been conducted on the subject based on the idea 6,7 , not much theoretical progress followed on it. In fact, the best parameter set for the multilayer coating model such as thicknesses of layers and choices of materials are not clear from a theoretical point of view. In this letter, the multilayered structure is carefully evaluated with a rigorous calculation on the electromagnetic field distribution to keep its self-consistency. The resultant vortex-penetration field, the best combination of parameters, and materials are described.The multilayer coating model 3 consists of alternating layers of superconductor layers (S) and insulator layers (I). The simplest configuration with a single superconductor layer and a single insulator layer is seen in Fig. 1. Each S layer is expected to withstand higher field than bulk Nb, and to shield the bulk Nb from the applied RF surface magnetic field B 0 , because B i (the RF surface field on the bulk Nb) is smaller than B 0 . Then the multilayered structure is thought to withstand a higher field than the bulk Nb if B 0 is smaller than the vortexpenetration fields of the top S layer and B i is smaller than that of the bulk Nb. The vortex-penetration field of the S layer was given by B v = φ 0 /4πλξ in the original a) kubotaka@post.kek.jp paper 3 , where φ 0 = 2.07 × 10 −15 Wb is the flux quantum 8 , and λ and ξ are a Lo...

Theory of the superconductor-insulator-superconductor (S-I-S) multilayer structure in superconducting accelerating cavity application is reviewed. The theoretical field limit, optimum layer thicknesses and material combination, and surface resistance are discussed. Those for the S-S bilayer structure are also reviewed.