Physics – Condensed Matter – Superconductivity
Scientific paper
1996-10-25
Physics
Condensed Matter
Superconductivity
8 Pages, RevTeX, 3 Postscript figures
Scientific paper
10.1103/PhysRevB.55.6015
In this paper we derive effective boundary conditions connecting the quasiclassical Green's function through tunnel barriers in superconducting - normal hybrid (S-N or S-S') structures in the dirty limit. Our work extends previous treatments confined to the small transparency limit. This is achieved by an expansion in the small parameter $r^{-1}=T/2(1-T)$ where T is the transparency of the barrier. We calculate the next term in the $r^{-1}$ expansion for both the normal and the superconducting case. In both cases this involves the solution of an integral equation, which we obtain numerically. While in the normal case our treatment only leads to a quantitative change in the barrier resistance $R_b$, in the superconductor case, qualitative different boundary conditions are derived. To illustrate the physical consequences of the modified boundary conditions, we calculate the Josephson current and show that the next term in the $r^{-1}$ expansion gives rise to the second harmonic in the current-phase relation.
Lambert Jean-Charles
Raimondi Roberto
Sweeney V.
Volkov A. F.
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