Theory of the Josephson effect for linked, mesoscopic superconducting dots

Abstract

We examine quantum properties of mesoscopic, weakly coupled superconducting dots, in the limit that charging effects and quantization of energy levels within the dots are negligible, but quasi-particle transmission into the weak link is not. We demonstrate that quasi-particle resonances lead to current-phase relations, which deviate markedly from those of weak links connecting macroscopic superconductors. In particular, the current I(ϕ) is no longer an odd function of the phase ϕ and the phase average of I(ϕ) over an interval 2π does not vanish. Results for the steady state dc Josephson current of two coupled dots are presented.