Complex Dynamical Flow Phases and Pinning in Superconductors with   Rectangular Pinning Arrays
  We examine vortex pinning and dynamics in thin-film superconductors interacting with square and rectangular pinning arrays for varied vortex densities including densities significantly larger than the pinning density. For both square and rectangular pinning arrays, the critical depinning force shows maxima at only certain integer matching fields where the vortices can form highly ordered arrays. For rectangular arrays the depinning force and commensurability effects are anisotropic with a much lower depinning threshold for vortex motion in the easy flow directions. We find evidence for a crossover in pinning behavior in rectangular pinning arrays as the field is increased. We also show analytically, and confirm with simulations, that for $B = 2B_{\phi}$ the strongest pinning can be achieved for rectangular pinning arrangements rather than square for one direction of driving force. Under an applied driving force we find a remarkable variety of distinct complex flow phases in both square and rectangular arrays. These flow phases include stable sinusoidal and intricate pinched patterns where vortices from different channels do not mix. As a function of the driving force certain flow states become unstable and transitions between different phases are observed which coincide with changes in the net vortex velocities. In the rectangular arrays the types of flow depend on the direction of drive. We also show that two general types of plastic flow occur: stable flows, where vortices always flow along the same paths, and unstable or chaotic flows. 
C. Reichhardt, G.T. Zimanyi, and N. Gronbech-Jensen