Critical currents and vortex states at fractional matching fields in superconductors with periodic pinning - art. no. 054510

We study vortex states and dynamics in two-dimensional (2D) superconductors with periodic pinning at fractional submatching fields using numerical sim ulations. For square pinning arrays we show that ordered vortex states form at 1/1,1/2, and 1/4 filling fractions while only partially ordered states form at other tilling fractions, such as 1/3 and 1/5, in agreement with rec ent imaging experiments. For triangular pinning arrays we observe matching effects at filling fractions of 1/1, 6/7, 2/3, 1/3, 1/4, 1/6, and 1/7. For both square and triangular pinning arrays we also find that, for certain su bmatching fillings, vortex configurations depend on pinning strength. For w eak pinning, ordering in which a portion of the vortices are positioned bet ween pinning sites can occur. Depinning of the vortices at the matching fie lds, where the vortices are ordered, is elastic while at the incommensurate fields the motion is plastic. At the incommensurate fields, as the applied driving force is increased, there can be a transition to elastic flow wher e the vortices move along the pinning sites in 1D channels and a reordering transition to a triangular or distorted triangular lattice occurs. We also discuss the current-voltage curves and how they relate to the vortex order ing at commensurate and incommensurate fields.