Theory of planar ballistic SNS junctions at T = 0

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Abstract
This Letter presents the theory of planar ballistic superconductor–normal metal–superconductor junctions at T = 0 for any normal layer thickness L taking into account phase gradients in superconducting leads. The current-phase relation was derived in the model of the steplike pairing potential analytically and is exact in the limit of large ratio of the Fermi energy to the superconducting gap. At small L (short junction) the obtained current-phase relation is essentially different from that in the previous theory neglecting phase gradients. It was confirmed by recent numerical calculations and was observed in the experiment on short InAs nanowire Josephson junctions. The analysis resolves the problem with the charge conservation law in the steplike pairing potential model.

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