Reversible vortex ratchet effects and ordering in superconductors with simple asymmetric potential arrays

Using computer simulations, we demonstrate that the simplest vortex ratchet system for type-II superconductors with artificial pinning arrays, a simple asymmetric potential array, exhibits the same features as those of more complicated two-dimensional (2D) vortex ratchets that have been studied in recent experiments. We show that the simple geometry, proposed by Lee [Nature (London) 400, 337 (1999)], undergoes multiple reversals in the sign of the ratchet effect as a function of vortex density, substrate strength, and ac drive amplitude, and that the sign of the ratchet effect is related to the type of vortex lattice structure present. Thus, although the ratchet geometry has the appearance of being effectively one dimensional, the behavior of the ratchet is affected by the 2D structure of the vortex configuration. When the vortex lattice is highly ordered, an ordinary vortex ratchet effect occurs, which is similar to the response of an isolated particle in the same ratchet geometry. In regimes where the vortices form a smectic or a disordered phase, the vortex-vortex interactions are relevant, and we show with force balance arguments that the ratchet effect can reverse in sign. The dc response of this system features a reversible diode effect and a variety of vortex states including triangular, smectic, disordered, and square.