Boundary conditions for the Eilenberger and Usadel equations and properties of “dirty” SNS sandwiches

Boundary conditions are obtained for the Eilenberger, Usadel, and Ginzburg–Landau equations at the sharp planar (specular) interface of two metals that have equal electronic masses and are in good electrical contact. These conditions are used to investigate the steady-state Josephson effect in quasi-one-dimensional “dirty” SNS sandwiches with an interlayer of “truly” normal with TcN = 0. It is concluded that the maximum values of the parameter Vc of such structures are attained in the case where the N interlayer consists of a high-resistivity metal of relatively low thickness d [γ <d/ξN≲1(γ = σNξs/σsξN;σN,s) and ξN,S are the conductivities and coherence lengths of the normal and superconducting metals].