Vortex Transport and Pinning Effectiveness in Conformal Pinning Arrays

We examine the current driven dynamics for vortices interacting with conformal crystal pinning arrays and compare to the dynamics of vortices driven over random pinning arrays. We find that the pinning is enhanced in the conformal arrays over a wide range of fields, consistent with previous results from flux gradient-driven simulations. At fields above this range, the effectiveness of the pinning in the moving vortex state can be enhanced in the random arrays compared to the conformal arrays, leading to crossing of the velocity-force curves.

Domain and Stripe Formation Between Hexagonal and Square Ordered Fillings of Colloidal Particles on Periodic Pinning Substrates

Using large scale numerical simulations, we examine the ordering of colloidal particles on square periodic two-dimensional muffin-tin substrates consisting of a flat surface with localized pinning sites. We show that when there are four particles per pinning site, the particles adopt a hexagonal ordering, while for five particles per pinning site, a square ordering appears. For fillings between four and five particles per pinning site, we identify a rich variety of distinct ordering regimes, including disordered grain boundaries, crystalline stripe structures, superlattice orderings, and disordered patchy arrangements. We characterize the different regimes using Voronoi analysis, energy dispersion, and ordering of the domains. We show that many of the boundary formation features we observe occur for a wide range of other fillings. Our results demonstrate that grain boundary tailoring can be achieved with muffin-tin periodic pinning substrates.

Strongly Enhanced Vortex Pinning by Conformal Crystal Arrays

Conformal crystals are non-uniform structures created by a conformal transformation of regular two-dimensional lattices. We show that gradient-driven vortices interacting with a conformal pinning array exhibit substantially stronger pinning effects over a much larger range of field than found for random or periodic pinning arrangements. The pinning enhancement is partially due to matching of the critical flux gradient with the pinning gradient, but the preservation of the sixfold ordering in the conformally transformed hexagonal lattice plays a crucial role. Our results can be generalized to a wide class of gradient-driven interacting particle systems such as colloids on optical trap arrays.