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$ $The critical current of a Josephson junction is an oscillatory function of the enclosed magnetic flux $Phi$, because of quantum interference modulated with periodicity $h/2e$. We calculate these Fraunhofer oscillations in a two-dimensional (2D) ballistic superconductor--normal-metal--superconductor (SNS) junction. For a Fermi circle the amplitude of the oscillations decays as $1/Phi$ or faster. If the Fermi circle is strongly warped, as it is on a square lattice near the band center, we find that the amplitude decays slower $propto 1/sqrtPhi$ when the magnetic length $l_m=sqrt{hbar/eB}$ drops below the separation $L$ of the NS interfaces. The crossover to the slow decay of the critical current is accompanied by the appearance of a 2D array of current vortices and antivortices in the normal region, which form a bipartite rectangular lattice with lattice constant $simeq l_m^2/L$. The 2D lattice vanishes for a circular Fermi surface, when only the usual single row of Josephson vortices remains.
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 functi
We calculate the beating of $h/2e$ and $h/e$ periodic oscillations of the flux-dependent critical supercurrent $I_c(Phi)$ through a quantum spin-Hall insulator between two superconducting electrodes. A conducting pathway along the superconductor conn
Using tunneling spectroscopy, we have measured the local electron energy distribution function in the normal part of a superconductor-normal metal-superconductor (SNS) Josephson junction containing an extra lead to a normal reservoir. In the presence
The fractional Josephson effect is known to be a characteristic phenomenon of topological Josephson junctions hosting Majorana zero modes (MZMs), where the Josephson current has a $4pi$ (rather than a $2pi$) periodicity in the phase difference betwee
We report the realization and investigation of a ballistic Andreev interferometer based on an InAs two dimensional electron gas coupled to a superconducting Nb loop. We observe strong magnetic modulations in the voltage drop across the device due to