Calculation of T-c in a normal-superconductor bilayer using the microscopic-based Usadel theory

The Usadel equations give a theory of superconductivity, valid in the diffu sive limit, that is a generalization of the microscopic equations of the BC S theory. Because the theory is expressed in a tractable and physical form, even experimentalists can analytically and numerically calculate detailed properties of superconductors in physically relevant geometries. Here, we d escribe the Usadel equations and review their solution in the case of predi cting the transition eeo temperature T-C of a thin normal-superconductor bi layer. We also extend this calculation for thicker bilayers to show the dep endence on the resistivity of the films. These results, which show a depend ence on both the interface resistance and heat capacity of the films, provi de important guidance on fabricating bilayers with reproducible transition temperatures. Published by Elsevier Science B.V.