Edge critical currents of dense Josephson vortex lattice in layered superconductors

We calculate the field dependence of the critical current for the dense Josephson vortex lattice which is created by a large magnetic field B applied along the layers of atomically layered superconductors. In clean samples a finite critical current appears due to the interaction of the lattice with the boundaries. The boundary induces an alternating deformation of the lattice decaying inside the sample at the typical length, which is larger than the Josephson length and increases proportionally to the magnetic field. The exact shape of this deformation and the total current flowing along the surface are uniquely determined by the position of the lattice in the bulk. The total maximum Josephson current has an overall 1/B dependence with strong oscillations. In contrast to the well-known Fraunhofer dependence, the period of oscillations corresponds to adding one flux quantum per two junctions. Due to the interaction with the boundaries, the flux-flow voltage for slow lattice motion also oscillates with field, in agreement with recent experiments.