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

Victor C.Y. Chang, Chon-Saar Chu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The zero-temperature current-phase (I-φ) relation (CPR) of a mesoscopic, ballistic, and asymmetrically stacked, double superconductor-normal-metal-superconductor (SNS) junction is studied. Here φ 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 φ2 of the middle superconductor. We propose to determine the values of φ2 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 L2) 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 L2 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 LTotal in the normal regions and the same L2. This is in contrast with the greater sensitivity the CPR has to the changes in LTotal or L2.

Original languageEnglish
Pages (from-to)249-261
Number of pages13
JournalPhysica B: Condensed Matter
Issue number4
StatePublished - 20 Jul 1998


  • Andreev level tunneling
  • Current-phase relation
  • Cutoff feature
  • SNS junction

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