Superconducting current in a ballistic double superconducting–normal-metal–superconducting structure

Using the Bogoliubov–de Gennes equation, we study superconducting current in a ballistic double superconducting–normal-metal–superconducting (SNSNS) structure. There are two contributions to the current: current ${\mathit{I}}_1$ due to the discrete part of the excitation spectrum and current ${\mathit{I}}_2$ due to the continuous part of the spectrum. Bound states (Andreev levels) are associated to each normal region. If the length L of the middle S region is comparable to (or smaller than) the coherence length ${\xi }_0$, the Andreev levels in different regions interact; if L≫${\xi }_0$ the Andreev levels are noninteracting. The interaction between the Andreev levels influences ${\mathit{I}}_1$. Moreover, ${\mathit{I}}_2$ is negligible only in the limits L≪${\xi }_0$ and L≫${\xi }_0$. We present curves for the dependence of the critical current ${\mathit{I}}_{\mathit{c}}$ on L and on the pair potential of the middle S region. The pair potential of the middle S region prevents reduction of ${\mathit{I}}_{\mathit{c}}$. The effects we study will not be present in a transfer Hamiltonian approach.