Edge effects in the magnetic interference pattern of a ballistic SNS junction

We investigate the Josephson critical current $I_c(Φ)$ of a wide superconductor-normal metal-superconductor (SNS) junction as a function of the magnetic flux $Φ$ threading it. Electronic trajectories reflected from the side edges alter the function $I_c(Φ)$ as compared to the conventional Fraunhofer-type dependence. At weak magnetic fields, $B\lesssim Φ_0/d^2$, the edge effect lifts zeros in $I_c(Φ)$ and gradually shifts the minima of that function toward half-integer multiples of the flux quantum. At $B>Φ_0/d^2$, the edge effect leads to an accelerated decay of the critical current $I_c(Φ)$ with increasing $Φ$. At larger fields, eventually, the system is expected to cross into a regime of "classical" mesoscopic fluctuations that is specific for wide ballistic SNS junctions with rough edges.

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