Collective-pinning theory for magnetically coupled layered superconductors

We calculate the tilt modulus ${\mathit{C}}_{44}$ and make collective-pinning estimates for a vortex lattice in magnetically coupled superconducting layers. Complete analysis of possible pinning regimes is made. The tilt modulus has unusual nonlocal structure which leads to peculiar pinning behavior. Namely, under certain conditions for the pinning strength and the magnetic coupling, a transition from a regime of independently pinned two-dimensional (2D) vortex lattices in the layers to a state of three-dimensional (3D) collective pinning occurs as a first-order phase transition. The critical current in 3D collective-pinning regime has characteristic nonmonotonic field dependence.