  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.
