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We numerically investigate magnetization, pinning, ordering, and dynamics ofvortices interacting with pinning arrangements which have a density gradient.We focus on conformal crystal structures obtained by conformally transforming aspatially uniform periodic array, as well as non-conformal gradient structuresand structures with quasiperiodic order. The conformal structures feature adensity gradient and local ordering. Using magnetization simulations we findthat conformal pinning arrays exhibit enhanced pinning compared tonon-conformal gradient arrays as well as compared to random, periodic, andquasiperiodic arrays, for a broad range of fields. The effectiveness ofconformal arrays arises from the continuum of length scales introduced into thearrays by the conformal transformation, allowing for a broad range of localcommensuration effects. At higher vortex fillings above the range of conformaleffectiveness, we show that a non-conformal rectangular gradient array exhibitsstrong pinning due to a novel commensuration effect and vortex ordering. Usingtransport simulations where vortices are driven along the gradient and at anangle to the gradient, we confirm the effectiveness of conformal pinning atincreasing the critical current. For a rotated drive, the gradient arraysproduce a strong vortex guidance effect in the direction perpendicular to thegradient.

Pinning, Ordering, and Dynamics of Vortices in Conformal Crystal and Gradient Pinning Arrays