Josephson current in a SNS contact in the presence of a magnetic field

The superconducting current through a SNS contact situated in a magnetic field parallel to the interface between the normal metal and superconductor is calculated. It is assumed that the thickness of the normal interlayer d is considerably greater than the coherence length ξ0. The calculation is carried out for a model in which the ordering parameter is constant in each of the superconductors right up to the boundary, while it vanishes stepwise in the normal interlayer. It is likewise assumed that the magnetic field is constant in the normal interlayer and is equal to zero in the superconducting parts of the contact. The calculation is based on lowering the order of the Gor'kov equations for the Green's functions and on formulating the latter by the “splicing” method from two linearly independent solutions. The general results have a complex form, but a simpler expression has been derived for zero temperature: j¯=[jc(0)π2/2eHLd](Φ+2−Φ−2), where j¯ is the current density averaged over the cross section of the contact; jc(0) is the critical current through the contact in the absence of a field; H is the magnetic field; L is the transverse dimension of the contact; the functions Φ± are defined according to the equation Φ±=[(φ0±2eHLd/2π)−1/2]−1/2] in which [x] denotes the fractional part of x, while φ0 is the the field.

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