Edge effects in the magnetic interference pattern of a ballistic SNS   junction
  We investigate the Josephson critical current $I_c(\Phi)$ of a wide superconductor-normal metal-superconductor (SNS) junction as a function of the magnetic flux $\Phi$ threading it. Electronic trajectories reflected from the side edges alter the function $I_c(\Phi)$ as compared to the conventional Fraunhofer-type dependence. At weak magnetic fields, $B\lesssim \Phi_0/d^2$, the edge effect lifts zeros in $I_c(\Phi)$ and gradually shifts the minima of that function toward half-integer multiples of the flux quantum. At $B>\Phi_0/d^2$, the edge effect leads to an accelerated decay of the critical current $I_c(\Phi)$ with increasing $\Phi$. 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. 
Hendrik Meier, Vladimir I. Fal'ko, Leonid I. Glazman
cond-mat.supr-con cond-mat.mes-hall