Current-phase relation of a ballistic asymmetric double superconductor-normal-metal-superconductor junction

The zero-temperature current-phase (I-phi) relation (CPR) of a mesoscopic, ballistic, and asymmetrically stacked, double superconductor-normal-metal-superconductor (SNS) junction is studied. Here phi is the phase difference between the two superconducting end-electrodes. The lack of configuration symmetry in such asymmetric SNSNS junctions forbids a simple choice of values for the phase phi(2), of the middle superconductor. We propose to determine the values of phi(2), by equating the currents in the two normal regions. Two features in the CPR are found. First, the CPR of the asymmetric junction has a cutoff feature, whose origin is best demonstrated in the long middle superconductor (large L-2) cases, when the critical current of the double SNS junction is bounded by the SNS junction that has the longer normal region. This cutoff feature is more pronounced for longer L-2 and for higher degree of junction asymmetry. Second, in regions other than the cutoff region, the CPR of the asymmetric junction deviates only within a few percent from the CPR of the symmetric junction which has the same total length L-Total in the normal regions and the same L-2. This is in contrast with the greater sensitivity the CPR has to the changes in L-Total or L-2. (C) 1998 Elsevier Science B.V. All rights reserved.