Two-dimensional Josephson vortex lattice and anomalously slow decay of the Fraunhofer oscillations in a ballistic SNS junction with a warped Fermi surface

The critical current of a Josephson junction is an oscillatory function of the enclosed magnetic flux Φ, 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/Φ 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, 1/Φ, when the magnetic length lm=/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 ≃lm2/L. The 2D lattice vanishes for a circular Fermi surface, when only the usual single row of Josephson vortices remains.