Control of the supercurrent in a mesoscopic four-terminal Josephson junction

We study the control of the supercurrent in a mesoscopic four-terminal superconductor-normal-metalsuper-conductor (SNS) junction, in which the N region is a quantum dot connected via tunneling barriers to two superconducting electrodes and two normal electrodes, respectively. By using the nonequilibrium Green's function method, the current flowing into the quantum dot from each electrode is derived. We find that the supercurrent between two superconducting electrodes can be suppressed and even reversed by changing the de voltage applied across the two normal terminals, similar to recent experiments of diffusive SNS junctions and previous theories for both the ballistic and diffusive SNS junctions. Then we investigate a three-terminal SNS junction, reduced from the four-terminal junction by decoupling the dot from one normal terminal. We find that even at zero bias of the normal terminal, the supercurrent still can be controlled by changing the coupling strength between the dot and the normal terminal. In addition, both the Andreev reflection current and Andreev quasibound states depend on the phase difference of two superconductors and the coupling strength between the dot and superconducting electrodes. Finally, the behavior of the supercurrent is discussed in the limit when the normal terminals are decoupled from the system.